I'd say the weirdest glitch I've ever seen was in Fallout 4.
I was running around the Dugout Inn doing the quest there and noticed a NPC sitting eating his dinner (Or lunch... whatever) nothing too odd, then I noticed he was sitting the wrong way round, with the steak he was eating floating several feet off of the ground, without the plate which was sitting on the table being an empty plate on a table. The animation of the man eating was going normally... well except for the way he and his steak were positioned, the man's legs were through the back of the chair and the steak could be interacted with despite it floating. Ah Bethesda... your games are so big that there are tiny glitches that you never really fix because you can't find them in the code.