It turns out that both might be due to my character being a vampire.
I have only had three characters in Skyrim. Character No. 3 (Altmer, Male) spent his entire life as a Vampire (beginning at level 3, before the release of Dawnguard). He experienced both glitches described above. It was frustrating.
My big discovery was yesterday while beginning to play Dawnguard with Character No. 1 (Altmer, Male, Werewolf). He got the Guild Master armor/hood shortly before starting Dawnguard. Immediately before becoming a Vampire he could wear the Guild Master hood without the glitch; immediately after wearing the hood visually glitched. Apparently it wasn't because of the haircut.
Character No. 1 (Altmer, Male, Werewolf) and Character No. 2 (Orc, Male, Werewolf) both appropriately benefited from pickpocket enchantments. I would wager (but still need to confirm) that, like the thieves hood glitch, pickpocket enchantments now hurt odds when shortly before becoming a Vampire Lord they helped.
Any other glitches people have experienced as a Vampire? Just keep it informative so that people who play vampires know what to expect, and perhaps the Devs can address some of the issues.
Thanks!