Well if we're talking about glitches particularly in lego games, how about Lego Harry Potter years 5-7?
I think it's only on the Wii version, though I've seen next to no footage of this glitch in any capacity and don't have other copies of the game to compare, so I may be wrong about that, but anyway:
For context, in levels and also in the hubworld, you get a selection of different characters you can switch between, though you can swap out different characters in the selection via polyjuice potion while you're in the hubworld. To switch, you use the 1 and 2 buttons I think, it's been a while.
When editing a custom character, 1 and 2 have no other function, so when you're editing them, you can still switch, except it switches the custom character instead of the character you're playing, meaning you can actually edit real characters in the customizer. Sadly this effect reverses as soon as you enter a level and everything is reloaded, but there is some extra fun you can have with this.
The hubworld also has a cutscene viewer, and when you watch the cutscenes with the characters altered, the relevant character's player models actually remain altered in the cutscenes themselves. The possibilities are pretty much only limited by the amount of characters you can fit to change.
Sidenote, certain special models such as Fang can't be edited. Hagrid can, but only his coat with the skin customizer, meaning his coat can be turned into a white skull cloak