Take a bow Miko Mayama (Yeoman Tamula; A Tase of Armageddon). She was hilarously bad. Always looking nervous, looking to other actors for directions, not knowing where to stand, how to emote or how to interact with others. Not only that, but the terrible hokey accent.
Phyllis Douglas (Yeoman Mears; The Galileo Seven) also deserves a mention for one of the most desperate cases of over-acting seen on Star Trek.
I'm not sure who exactly the actress is, or what she played, but the alien in Virtuoso on Voyager was without a doubt dreadful.
As for the regulars, Avery Brooks is crap. Really crap. No, so bad it is embarrassing. Whenever he does the big angry speeches or touchy feely scenes his tone and pronunciation is so stilted it detracts. Maybe acceptable in theatre, certainly not for tv. He also had a tendency to overact.
Patrick Stewart is almost just as bad. Always the same accent, always the same pronunciation, always plays the same whenever acting. He really detracted from TNG. It was almost like Star Trek: Shakespeare. A good actor can adapt to different forms of dramatic mediums, it seems Stewart can't. I never got a Starship Captain from him, just a human Shakespeare actor trying to pay the bills on a sci fi show.
I used to think Jennifer Lien was crap. I've somewhat softened my stance recently. I think my hate for Kes was just out of control.
As for most unprofessional, Robert Beltran you are the winner. Just a shame he was never shoved out the airlock with Garett Wang.