I'm not on Twitter, but I think if a celebrity has a public Twitter or Facebook account, I don't see the problem.
Agreed. I am a fan of three celebrity pages (Zach Levi, Eliza Dushku, and Matthew Gray Gubler) on Facebook. I'm not sure why- I like their work, and then just seemed like interesting people, I suppose. I personally never reply to anything they post, but I do like seeing the updates of what they're working on (and sometimes some really strange and crazy drawings and photos from MGG.)
Eliza Dushku in particular regularly posts updates, pictures, and sometimes short videos to her fans. I don't see that any of them have very personal interactions with their fans; they post, hundreds and hundreds of comments are made, but the only one who ever really responds to something the fans post is Zach Levi.
If I were a celebrity, I'd probably have a page and post random items, but not read most of the comments. Some of the comments, especially for ED, are offensive and creepy. There are also the normal 5 gazillion "You are so hot and I want to marry you!" comments; as a celebrity I'd be sick to death of that after a while.
I think these types of pages are an easy way to "sort of" interact with fans while still keeping your distance (and possibly sanity).