I'm on the 360 with the actual RDR installed and Undead Nightmare is giving me some loading problems. I'll ride into a town and my horse (War) will skip ahead and "swim" through the ground. Then pop back up when the town's textures load in. 
 
I just got back into Blackwater from New Austin and the town wasn't loaded correctly with any detail and the "zombies" were just regular humans. I hit start and then went back into the game and the town  loaded right and the humans got their zombie layer. 
 
Animations skip and stutter when I loot corpses or open chests. 
 
The Map screen will come up without the actual map, just the controls. 
 
Occasionally I'll try and switch weapons but the game can't load that right either and Marston will just put up his fists...

Sounds like a typical stroll through RDR to me. Although they don't happen as frequent as maybe you're trying to convey, Undead Nightmare still does alot more glaring glitchs over the default RDR.

No, but I rode into... the town with the Marshal. I couldn't talk to him until after 30 seconds. Also, the texture streaming is not always fast enough. I've had a couple of cutscenes where the characters in the first five seconds had low quality textures on their face and hands, and it would suddenly just pop up with the proper texture.

Wow these types of issues sound like playing San Andreas back on the PS2??? I seriously never had ANY such issues with my hours spend in Red Dead. 
 
Could it be that since you are playing with the game installed you have loading problems as it must load both parts of the base game off and the addon both from the HDD? You could try deleting the install and playing off the disc and see if it helps.

Yeah I'm getting some bad lag here and there, which is strange because I never had a problem with the original.