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Ass Pull: The Hindmost reveals to Louis Wu in The Ringworld Throne that he has a quantum computer and the Nanotech-based autodoc invented by Louis' biological father Carlos aboard his ship, without having mentioned them at all in the previous book.
In Ringworld's Children, Louis discovers that Teela became a protector on one of the Maps of Pak in the Other Ocean, then traveled to the Map of Mars on the other side of the Ringworld and pretended to turn into a protector again for Bram's benefit. Apparently, the only reason for this is to justify why Wembleth lived near the Other Ocean.
Ringworld's Children also introduces the concept of monsters in hyperspace that take time to catch and eat spaceships, in order to explain how the entire Ringworld, 1 AU around its sun, can go into hyperspace without being immediately destroyed.
Canon Sue: In Ringworld's Children, Louis is transformed into a protector, but after using his new abilities to resolve the plot, he gets better thanks to Carlos Wu's autodoc. If becoming a protector is now a reversible condition, it diminishes the Blessed with Suck aspect that protectors have always had.
Never Live It Down: Because Red Herders are culturally monogamous, much of the conflict in the "Fearless Vampire Slayers" storyline in The Ringworld Throne comes from Tegger and Warvia fearing that they'd get a reputation for promiscuity after all the rishathra they had while under the influence of vampire scent.
Sequelitis: The Ringworld Throne and Ringworld's Children are arguably not as good as the first two books in the series because of the number of Ass Pulls required by the plot (see above). The Ringworld Throne also suffers from focusing primarily on the Fearless Vampire Slayers, with Louis spending most of the story only watching them over the Hindmost's video feeds.
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