Anticlimax Boss: The fight between Banagher and Loni was somewhat underwhelming for some fans.
Alas, Poor Villain: Seeing as how this is a Gundam series, this is a common trope since villains tend to be on the sympathetic or tragic side. One notable example, though, is Loni.
Loni: Banagher. It's sad, isn't it...?
Complete Monster: Martha Vist Carbine, who will use anyone from teenage girls and family members as political tools... and notinaniceway, either. She's pretty much the only villain so far presented without the slightest hint of sympathy (excluding Frontal, who's just too inscrutable).
Crowning Music of Awesome: Gundam Unicorn's score is probably the most intensely cinematic of any Gundam series, OVA, or movie so far, which says quite a bit when you consider that past composers include Yoko Kanno, Toshihiko Sahashi and Kenji Kawai.
Dying Moment of Awesome: Daguza, oh so much. He first catches the Sinanju in a trap of bombs, then hits the thing in the face with a bazooka. Faced with Full Frontal's retaliatory beam saber attack, he turns around and gives Banagher a last, unflinching salute before being completely incinerated. The man was truly a living incarnation of badass.
Ensemble Darkhorse: The unnamed Stark Jegan pilot who nearly owns the Kshatriya in the first 6 minutes of the first episode.
Not only did he manage to hold his own against the Kshatriya, but the Stark Jegan's HGUC manual implies that he was one of the guys that attempted to help Amuro push back Axis three years prior. The guy was a true hero.
The name, though extremely narmy, likely has some kind of ironic and fairly witty symbolism. Full Frontal implies being "bare naked" or "fully exposed" (*COUGH* ...Which really doesn't help the Narm factor) while in reality the character wears a mask and is very mysterious.
Also, Full Frontal, "full frontal assault," as in a full-on, all-out assault, so it also doubles as a shout out to the missing-in-action Char Aznable's combat style.
On the other hand, he is aping a guy who spent a couple years going by the name Quattro  Bajeena.
A rare few moments in the surprisingly competent English dub sounded somewhat phoned in, particularly Marida Cruz's VA's reading of the line "So heavy." being utterly narm-tastic. (Although that might have to do with the line being an awkward one in-and-of itself, being a direct translation of the Japanese audio.)
Episode two looks to continue this tradition further. "That's the See-non-jew."
Daguza: You are my hope. It's all up to you now, Banagher.
Gilboa: Tikva... Just look after the family for me...
Cardeas: Please forgive me. I wanted more... so much... Banagher... My wish has finally come true... Anna...
Two instances in episode 5:
Zinnerman trying to get Marida to remember who she is, and revealing that he considered her a surrogate daughter. He then breaks down saying that he doesn't want to lose his daughter and be alone again.
When trying to connect a tow cable to the Garancieres and risking getting his mobile suit torn in half, Banagher gets silent encouragement from the spirits of Daguza and Gilboa.
True Art Is Angsty: Gundam Unicorn currently has a lot of acclaim, and it's one of the darkest works in the franchise so far.
The Untwist: From the moment the first details about the novel came out, people already knew that Audrey was a teenaged Mineva Zabi, thanks to factors like her appearance, her age matching up with Mineva's, the latter's mysterious disappearance at the end of Zeta Gundam, and the obviousalias.
Another contributing factor is that the score playing when Audrey escapes the Sleeves ship in the first episode is titled "Mineva".
WTH? Casting Agency: Not casting exactly, but the fact an avowed Japanese Imperialist author like Fukui is writing the novels is rather odd considering the blatant anti-war & anti-Axis themes of previous UC series. For perspective, it's a bit like having a sequel to Maus written by the guy who did The Turner Diaries.
Not a full WTH, but fans were rather confused when it was discovered that Chieko Honda would not be voicing Marida Cruz, despite the fact that 1) she played both Purus in Gundam ZZ, and 2) she's still doing voice acting.
The fact that the Puru clone in question is now an adult and thus have a somewhat different voice may have something to do with it.
Though it's not like she hasn't voiced older women in Gundam before.