The Artifact: Leon, who popularity has allowed him to continue staying with Larry long after any story point justifies his existence. After the rest of his family leaves, Leon ignores Larry's hints and continues to freeload off of Larry. Only in one later episode does Larry finally try to get rid of Leon, but his ploy backfires.
Mary Sue: Subverted to hell and back. Larry is a deeply flawed character who people, quite rightfully, cannot stand most of the time. While there are occasions that he is sympathetic, he commits acts which are pretty much inexcusable from any viewpoint (he once nearly let Jeff and Susie's daughter drown because he didn't want to damage his blackberry and deceived his cancer-stricken girlfriend into leaving him).
Never Live It Down: Bill Buckner in-story. 25 years after committing a mistake that cost the Red Sox the World Seriesnote (actually cost them Game 6, tying the series and necessitating a Game 7, which Boston lost), everybody still hates him for it.
Strawman Has a Point: Larry is almost always the object of scorn and derision for his actions and opinions, but a fair bit of the time the audience is meant to sympathize with his refusal to go along with various abritrary and capricious rules of "polite" society, believing that Larry is typically in the 'right'.
They Wasted a Perfectly Good Plot: While the eighth season was touted as the "Larry in NYC" season, only five of the ten episodes feature this setting, with the rest taking place in L.A. as usual.