I want him to come along but I can't do some quests because occasionally he sets people off indoors. They start talking to him saying, "You need to leave," over and over and over (yes, him, not me). How do I fix the Imp Dog? If I petty crime and clear my name the guards take Barbas away from me. Like I said I don't want to loose him.

I'm not sure that's possible, NPCs can't really trespass as far as I know, so you sure they're talking to him and not you?

I would just finish the quest "A Daedra's Best Friend", that way he won't be following you all the time anymore and causing glitches. Or is it that you want him to be a permanent follower? If so, there are several other dogs that you can use as a follower, but none of them, obviously, are invincible like Barbas.

He will likely eventually get stuck in some location if you keep him as a permanent follower, I have experienced it myself (during the "Lights Out" quest in the Blackblood's hideout, Broken Oar Grotto, near Solitude). I don't think he is really designed to be anything, but a temporary follower.

Hah, whaaat! I knew those random poachers were the only NPCs who talk to animals.