Bellisario's Maxim: The season one episode "Trespass", which occurred on an ice-world, featured a scene with a group of native Talz huddled around a fire. According to the special features, the writers and producers have been bombarded with questions asking what the Talz were burning, more-so from people involved with the production than even rabid fans, and they can not give an adequate explanation. They quote the maxim almost verbatim, and explain that this is something that people really should not think about.
Cad Bane became one of the most popular characters in the series, as an Expy of Boba Fett with a cool voice, unusually sinister tendencies, and characteristics of spaghetti-western villains.
Hondo Ohnaka is starting to become one of these.
The mercenary Embo from "Bounty Hunters" was a One-Scene Wonder with acrobatics to make a Jedi jealous, a Nice Hat that serves as a blaster-proof shield and as a Precision-Guided Boomerang. Despite being a relatively minor character in one of the less important episodes of the series, he's popular enough that he got his own action figure.
Savage Opress is quite popular too. The fact that he's Darth Maul's brother help.
Family-Unfriendly Aesop: In the "Citadel" trilogy, Ahsoka sneaks in with the team against direct orders not to do so, then lies about it, insisting that another high-ranking Jedi authorized her to go. At the end even though she does confess her lie to a dying member of the team, Jedi High Council Member Plo Koon covers up for her, saying that he did indeed sent her on the mission. So not only does she face no punishment or any consequences at all for her actions and lie (which Jedi aren't supposed to do anyway), she has adults covering up for her before authority. Make sure you learned this week's lesson, kids!
Fan-Preferred Couple: Ahsoka/Rex (or Rexsoka, if you wish) remains the most popular Ahsoka pairing, even though she has a canon love interest in the form of Lux Bonteri. This is probably because Lux is comparatively new on the scene, and Rexsoka was already well-established in the fandom before his episode premiered in Season 3. Karen Traviss and Karen Miller's teases towards Rexsoka in the novels did not help things.
Asajj decides to strip off most of her outfit during her fight with Kenobi. Supplementary materials say that she gets pretty obsessed with Obi-Wan over the course of the war. His retort when she tries to distract him by throwing said clothes in his face? "You'll have to do better than that, my darling." They continue this "flirtation" several more times, but it seems Obi-Wan, at least, is being sarcastic.
Despite Barriss Offee's Face Heel Turn, she still has a popular ship with Ahsoka.
Growing the Beard: Despite complaints on various things, the biggest being the cartoony Battle Droid humor, the series has been very well received after the first season (and even a few first-season episodes are well-liked). The first episode to shuffle that humor aside, and coincidentally one of the more popular episodes, was "Rookies", which introduced the efficient Droid Commandos. Despite the droids eventually losing it was a step forward in maturity and threat level for the series. The later episode "The Hidden Enemy" is also cited for the same reasons, the droids are more intimidating when using zero-humor swarming tactics.
Harsher in Hindsight: Episodes 15-18 of Season 4 are about Obi-Wan going undercover to uncover a Separatist plot against Chancellor Palpatine. On January 26th, the day before the second episode in the arc premiered, Ian Abercrombie (Palpatine's voice actor) passed away.
Also, remember the Father's warning to Anakin when he refused? That his selfishness would haunt him and the galaxy at large for refusing to replace the Father? Although at the time the episode was made, they probably were intending to mean the oncoming Jedi Purge, but after the revelation of Abeloth's ties to the Ones in the final book of Fate of the Jedi: Apocalypse, as well as what Abeloth did throughout that series, the Jedi Purge actually seemed not so bad in comparison.
Hilarious in Hindsight: The second episode of Mad TV has Gary Anthony Williams doing a parody of Count Dooku (or "Count Poo-Poo"). One year later, he is voicing Riff Tamson, one of Dooku's subordinates, on The Clone Wars.
Jerkass Woobie: Asajj Ventress. Even discounting her Dark and Troubled Past, and even though she's an evil, vengeful psychopath, she's had a rough go of it. Frequent failures, betrayed through no fault of her own, utterly failed to gain retribution for said betrayal, and has now lost everything she ever worked towards or cared about. Even after everything she's done, seeing her break down and beg Mother Talzin not to leave her alone is still quite the Tear Jerker.
Darth Maul. Bisected and left for dead, and somehow made his way to a hellish, fiery scrap pile of a planet, only to be crudely attached to a nightmarish spider-like machine and go almost completely insane over the next decade. Even for an evil, Badass Sith Lord, seeing him reduced to a crazy, sobbing wreck engenders quite a bit of sympathy.
Magnificent Bastard: Palpatine's maneuverings during episodes like 'Destroy Malevolence' where he sends Padme on a diplomatic mission that just so happens to lead her right into General Grievous's hands; 'Heroes on Both Sides' where he discovers that Mina Bonteri is responsible for sponsoring the Separatist bill to end the war and her subsequent fate, etc. seem to show that the guy can play the odds and adapt like only a Magnificent Bastard could.
An inordinate amount of people seem to think that George Lucas is responsible for any problems with this series. Dave Filoni is the real frontman of the project. To be fair, whole episodes have been written on Lucas' orders, and Dave Filoni has also implied that the show would be rather different if Lucas had not unexpectedly become responsible for its production.
Likewise, some misblame Filoni or other writers for disregard of certain EU elements, when, by their account, Lucas exercised Executive Veto power.
Asajj Ventress flies past it on hyperdrive, when she goes to recruit an assassin against Count Dooku. Particularly when she tests the brainwashing of the chosen candidate by ordering him to kill his brother. This strikes the viewer even harder, as before that Ventress was almost (sym)pathetic, due to her constant failures.
Pong Krell crosses it when he states that Jesse and Fives will be court martialed, found guilty, and executed. Worse still, when Rex tries to argue against it, he just decides to straight-up execute them without trial.
He crosses it yet again he manipulates the clones into killing each other. When confronted on this, he reveals he's actually been a traitor the entire time.
Pre Vizsla crossed his by ordering the burning of a village that Death Watch had been terrorizing, simply because they demanded the return of the women he had kidnapped, particularly the chief's daughter. Not only did he burn down the village and kill countless villagers, he started the massacre by returning the chief's daughter, only to stab her in the back immediately afterwards.
Darth Maul murdering a village full of innocent people to get Obi-Wan's attention.
Darth Maul: In a galaxy at war, Savage, the only way to draw the attention of the Jedi is with the slaughter of the innocent. Mercilessly, and without compromise.
No Yay: Even Cad Bane had hints of this with Ahsoka, but the most obvious example would be the way Garnac, the leader of a Trandoshan hunting party acted towards her. If the whole kidnapping Jedi children to hunt them down thing wasn't clear enough, he provides lines like these:
Garnac She (Ahsoka) can't hide for ever! Mark my words, I'll have her skin, and nail it to the wall for killing my son!
Garnac A valiant effort, little younglings. Especially you, Togruta. You'll be a prized trophy of my collection.
Pandering to the Base: David Filoni acknowledged the negative reaction from the first half of the third season (which was focused on heavily on politics, trade blockades, bank interests, and stuff like that) and said that the amount of such episodes will be severely cut down.
Jar Jar Binks. Yeah, you read that correctly, no mistake - [they successfully rescued Jar Jar Binks from the scrappy heap. As of season four, arguably the entire Gungan race as well. In the episode "Shadow Warrior", they take down ''General Grievous'', albeit only when Captain Tarpals pulls a Heroic Sacrifice, successfully incapacitating him and allowing him to be captured.
Also, Anakin. Originally a Base Breaker in the movies, he's far more unanimously liked in the series due to his stronger characterization, his decreased tendency for Wangst, and Matt Lanter's voice acting being more well-received than Hayden Christensen's acting.
Ahsoka started out with similar levels of hatred to Jar Jar Binks (mostly for her Mary Sue and Spotlight-Stealing Squad tendencies), but her flaws have been toned down considerably, to the point that (in a bizarre inversion of sorts) some of the show's detractors actually label her as the only good character in the series. When she left the show, Ashley Eckstein said that some of the people who were the saddest about this had once been giant Ahsoka haters.
Strawman Has a Point: In "Corruption", Duchess Satine of Mandalore is shocked to discover just how far corruption has spread throughout her government. When she, Padme and her guards manage to find and apprehend smugglers bringing in tea which they have diluted with toxic chemicals, she orders the entire facility burned to the ground. The commander of the police protests that there is evidence in the building, but Satine explains that if he does not comply she will consider him a co-conspirator with the smugglers and then she goes off to find out just how high this conspiracy reaches. His initial disinterest in investigating her accusations certainly was suspicious, but by ignoring his advice and burning down the building Satine has eliminated any chance of finding records or documentation listing who was involved in the smuggling program, physical evidence placing people at the scene, etc. For a person who claims she is interested in following the web back to its source, Satine ignores rather legitimate points about proper criminal investigations.
Temporary Scrappy: After R2-D2 is lost in battle, Anakin is distraught over losing a friend, while Obi-Wan dismisses R2 as a "dime-a-dozen" droid. Ahsoka gets Anakin a new droid, R3-S6 ("Goldie"), who seems vastly inferior, and she doesn't make anything better by saying that the R3 models are supposed to be better. And in the end R3 turns out to be The Mole.
Pong Krell serves as one both in-universe and out in the Umbara arc. Cartoon Network's ads even outright say that Krell is not as cool as Anakin.
Tough Act to Follow: No matter how good any episode of Rebels and Resistance can be, The Clone Wars will always be viewed as the best animated Star Wars by the general audience and the loyal fanbase. Helps that it's the only series of The New Tens that's canon to the old Star Wars Expanded Universe which many fans regard as superior to the Disney era.
"Duel of the Droids" gives this to all sides. The clones throw a shock grenade at a group of commando droids, who reasonably attempt to shoot it so it doesn't go off (which fails). Then the clones do the same to a group of regular battle droids who had just witnessed this, and they proceed to pick the grenade up as if it's a mysterious device. On the side of good, Anakin's entire team continues to rely on the R3 unit which has done nothing but fail horribly at every task it is assigned, often managing to do the opposite (because it is actually programmed to sabotage their efforts). Even Anakin, who makes no bones about his dislike of the droid, doesn't have the common sense to just exchange it for one which isn't grossly incompetent. It's not like he couldn't do so, either; there's on a military vessel loaded with everything they could need, including replacement droids.
Pre Viszla deciding to engage a Jedi in a lightsaber duel was probably not the most intelligent thing he ever did.
He did it again in season 4 and almost shares Boba Fett's fate (malfunctioning jetpack, anyone?). In his defense, though, he did go straight for the "undignified execution" route at first. His quarry just happened to get free.
The Woobie: Anakin, Obi-Wan, Fives, Waxer in the Umbara Arc, and Rush Clovis.
WTH? Casting Agency: Simon Pegg being the voice of Dengar in the season 4 episode "Bounty". This is a man who's known for his hate for the prequel trilogy, special editions of the original trilogy, and The Clone Wars series itself, and he takes every opportunity he can to bash anything Star Wars post-1983, and the fact that he's getting rewarded for all his hate elicited this reaction from the die-hard Star Wars fans.