I'm already planning on having the Exhaustion Timer, Hunger Bar, and Thirst Bar disappear if they're currently irrelevant. Right now I see no reason why any HUD element shouldn't disappear when it's irrelevant.
For example, if you have perfect stamina at the moment, there's no reason to have it on screen. (Naturally, if your blood bar isn't perfect than you inherently have less-than-perfect stamina.) Same goes for concentration and ability.
Additionally, the compass shouldn't show up on the minimap if the character doesn't own a compass. If the character has no idea where they are, the minimap should be blank and the map screen shouldn't have a compass cursor on it. The minimap shouldn't show up at all if they don't have a map of some kind.
If the character has had all the items in a quick switch temporarily (as part of the storyline) taken away from him, the relevant "quick switch" should be invisible during gameplay, but not deleted. It should still show up as grayed out on the Customize GUI screen. If a quick switch becomes voluntarily irrelevant, (such as by dropping, selling, or removing all the items in it) the game should ask if they want to delete the quick switch. (They might not want to if they're simply upgrading the quick switch with better equipment.)
All elements should fade in/out when they change relevancy, NOT animate or pop up.
The thought ticker should never be hidden, as even if the character is talking at the moment the thought ticker would display subtitles.