As a former infant caregiver/daycare teacher I've had my share of biters. It does sound like the teachers are not watching as diligently as they should. You can't turn your back on a biter at any time! So I'm wondering what is triggering the biting, is he not getting his way, is he bored, did the other child have a toy he wanted etc. If you can figure out the trigger you may be able to help curb the behavior.
I don't necessarily agree with biting him, that could backfire by sending the wrong message and making him angry. Then he may bite when he is angry. I know in some cases where it worked and others where it just made things worse.
As far as the parents of the other kids just talking to them and apologizing may be enough. Maybe you can arrange a play date for the kids to make up and have Alexander apologize. (maybe not if they are not receptive.)
You may find some more helpful info and support at www.babycenter.com there are tons of great articles and message boards. I searched for biters and this is what I found:
http://www.babycenter.com/search/showResultsForContent.ht...
Good luck! I'm sure you will find something that works!
Edit
I wanted to add one more thing, I hope you told the director how his teacher kept referring to him as terrible. She should be ashamed of herself. A teacher should never refer to a child that way, and definitely not over and over. I had my share of terrible 2's and 3's but it's all the way you handle them. Children don't come out of cookies cutters there is no one way to handle a child, you have to adapt and meet each childs specific needs.
Hang in there, I'm sure things will get better. (Maybe a new daycare is in order?)