My character sheet shows attacks per round with a ranged weapon. When I turn on the rapid shot feat, all of the attack values go down, but there are still only three attacks showing. Is this a bug, or is three the maximum number of attacks that can be shown, so the others are there but just invisible?

I don't remember how this feat works exactly, but you can check it out easily. Just count the amount of attacks your character executes in 6 seconds starting from the beginning of the fight. You say that your ranger can do 3 attacks per round. If he executes 4 attacks in 6 second, this means that the feat works properly with your build.

Compare how much ammunition you have before and after the round. That should let you know whether attacks just aren't appearing.

It is not bugged, just one of the many poor showings in NWN2. The extra attack is made at the end of the round. You can read about it here