Berserk Button: Messing with any of his Ellie-related treasures. When he fulfills the adventure he promised Ellie, he overcomes this and throws the vast majority of the treasures out of the house so it's light enough for him to go after Russell.
Death Seeker: It's strongly implied that this was what motivated Carl to finally go to Paradise Falls, at least at first. After all, with Ellie dead and having no family left to speak of, what better way to go out in style than to do the one thing he was still able to pull off? Even if he knows that it'd likely be a one-way trip that could go terribly wrong.
Gadgeteer Genius: Carl qualifies, given he outfitted his house with shower curtain sails and a steering system. Carl retrofitted his entire house into an airship in less than one night. He's better than MacGyver!
Tragic Keepsake: The bottlecap "badge", Ellie's Adventure Book, her photo, the house itself... and the airport passes Carl was going to surprise her with just before her final hours. Really, a huge part of the plot is based around this trope and Carl's need to let go of them.
Ax Crazy: It may not be clear at first, but when he strongly implies that he's actually murdered others in the past just because he was paranoid that they were after his bird, AKA Kevin, it's quite obvious he's gone completely insane after all those years of searching to no avail. And he only gets worse. By the end of the movie, he attempts to kill Kevin, Dug and Russell (a 'kid' mind you), in cold blood with a shotgun.
Berserk Button: Kevin. Because he's been trying for well over sixty years to capture her, you'd do well to try and steer clear of both of them, if you know what's good for you...
Evil Counterpart: To Carl. Both of them were fixated on the past, and on living their adventure. One was able to move on, the other wasn't.
Expy: Charles Muntz was modeled after Charles Lindbergh, right down to the nose.
Face Heel Turn: After being called a fraud, he returned to Paradise Falls to capture the bird, and after many, many years of failures, he obviously lost sight that keeping the bird with her family was more important than proving himself.
Like a Son to Me: One Word Of God interview says that Russell was designed to be the child Ellie and Carl were unable to have, in both a figurative and literal spirit. Figurative in that if they had had a child, that child would be very much like Russell (especially at the end when he has both a mother and father figure in his life), and that Russell fills the hole Ellie left behind when she died, much like Carl and Ellie's potential child would have. Literal in that if you look close enough, Russell has features VERY similar to that of both Ellie and Carl...
The Load: Russell is responsible for every bad thing that happens in this movie (aside from the few Muntz does himself). Probably meant to be an inversion of how in many films where a crotchety old man is paired up with a spunky kid, it's the adult who's portrayed as inept and in need of rescue. Plus, Russell has the excuse that he has no real way of getting home under his own power. If Carl doesn't do it, the poor kid is toast.
Motor Mouth: Carl tries to get him to play "Who Can be Quiet the Longest":
Dumb Is Good: Dug is noticeably stupider than all the other dogs, who can talk in complex sentences and even, in at least one case, cook. The dogs themselves are not that intelligent, but they're still smarter than Dug.