automatic transmissions, any problems with them?

lots. what is your concern? Roy

overdrive went out and now transmission is slipping. will a trans flush and new filter fix the problem?

A flush might help. I bought mine used (and neglected of course lucky me) and had to replace the tranny several months after getting it. Make sure you keep up on replacing the fluid every 60,000 or whatever it is. I put 50,000 more miles on and haven't had a single issue with the tranny. Time for another flush.