Should the GM have a say over the number of players in his game? Sure, that can impact a game heavily. Should the GM have a say over personalities of players? IMO, to an equal extent as any other player.
Hmm, maybe if it's some kind of rotating GM system where the group is more important than the individual game/campain, or a shared world or somesuch.
Back in the old days I remember we used to interview prospective new players, typically the GM plus 1-2 current players would talk to a new prospect and see if they'd fit in. These days I run at a Meetup and if I have space anyone can join my game initially, but if they don't work out I may have to ask them to leave. That used to happen a lot in my 3.5e game, I suspect the 3e ruleset might be partially to blame as I've seen far fewer problems in my 4e game.