when you don't think their friendships are healthy?

[Notmyidea]

I loathe dd's "best friend" with a passion at the moment. She's always been an entitled little madam but as she's getting older it's getting nastier. She routinely puts dd down, calls her academic ability and interests "geeky," calls her fat then insists she's only joking (dd is perfectly balanced on the 75th centile for height and weight, "friend" is a similar height but much more slightly built) and generally seems to want to undermine her at every turn, (e.g. Discouraging dd from auditioning for the school play, disrupting other friendships...I could go on. I've had enough but dd adores her:(
How do I get dd to see there's a problem?

TBPH, I don't think you can. I know my DD had one or two unsuitable friendships in her last year of junior school, fortunately I knew we were moving to a different country so I just let them be.
Currently, she has a friend who she sometimes likes, sometimes loathes. I am ambivalent about the child and refuse to be drawn into the arguments.
In your situation, I think I'd be trying to widen her social circle, encouraging after school clubs, out of school clubs and possibly inviting other girls over to play after school.

I don't think that you can stop your DD seeing her friend, but I do think that it is the right time to teach her about healthy relationships, and people who make her feel bad about herself.

Like Rips said, I'd be looking to find alternative friends, and would try to limit time that she spends with her best friend.