Yes a dislike button is a must! I thought the star was me favouriting a tweet. I can see it but the person who's tweet is can't see that I have done that. I could be wrong though and like you say Facebook like is not for everyone anyway.
The dislike button has been suggested many times (and I think I have even seen fb groups demanding one). I think the reason they don't implement it is quite simple: it would damage the feel-good atmosphere. Imagine downvotes on new profile pictures or excited status updates.
Imagine if "Dislikes" exceeded "Likes" of a particular marketing campaign...