Over the course of the past few months I've managed to accumulate a collection of most of the clipping problems with assorted costumes and armor pieces alike - Considering they are all cosmetic, and with how many there are, I decided to make a neat, organized thread instead of spamming the reporting system in-game. The majority of these are very glaring and irritating to look at, and some aren't supposed to be a thing at all!

[All images are under a 'spoiler warning' to prevent page stretching.]

"Ebon Armory" Armor set: Both Khajiit and Argonian claws, on the hands and feet, clip through the gauntlets and sabatons of this set.
"Cavalier of the Sworn Oath" costume: This doesn't seem to affect Argonians, but for Khajiit there seems to be a clipping problem with this costume where the tail is. This is by far the most glaring issue I've seen so far when it comes to costume clipping, as this is the main costume I use on my Khajiit. It becomes most obvious on female Khajiit, as a brown 'gap' of sorts appears above, next to, or around the tail when they walk/run and ride mounts. For males, this seems to only appear when walking/running.
"Shrouded Armor" costume: Both Khajiit and Argonian toe claws clip through the boots of this costume.
"Glenmoril Witch Robes" costume: When using the walk animation, the legs of the player character clip through the back of the robes.
"Old Orsinium Sentry" costume: The bear head on this costume has somehow been stretched to be far wider on Khajiit heads than it should be. (After testing it on an Argonian, two Khajiit, a Dunmer, and a Breton, I can confirm that this only affects Khajiit, both males and females.)
"Pirate Sash and Bandolier Garb" costume: On male characters only, the part of the sash that hangs down over the leg is detached from the rest of the sash and moves around awkwardly against the leg, clipping through the pants. Most obvious when moving or using a personality.
Guild Tabards: On most guild traders who wear a basic shirt, the tabard clips through the lower half of the shirt that is under the belt.
Now for my last one - it's very minor, but since it counts as an animation error, I may as well throw it in here anyways.

"Merchant Lord's Formal Regalia" costume: When using the 'Cheerful' personality, the golden tips of the boots clip through the foot.