Nog on the Defiant's bridge - Again, I can buy his presence by the fact that Sisko chose him to be there. However, it would have been better if they waited until he was made an actual ensign. The idea of a cadet having that important of a role is a little hard to accept.
...
Wesley Crusher - Why was this kid given such an important role on the freaking flagship of the Federation? As stated above, it would have been better if he was assigned to the Engineering Department. That is, supposedly, where his strengths were supposed to be. The Traveler said he was "a Mozart of Engineering."

So, why was he flying the ship?