The text does indicate that keys are used by Morocco and Aragon to open the first two caskets, and that Bassanio is able to simply open the lead casket without a key. I would assume that this is Shakespeare's way of letting his audience know that Bassanio has chosen correctly and that there is now no impediment to his having Portia (as if the audience hasn't already figured this out by now!). Perhaps the keys are symbolic of the fact that she is still locked away from the men who choose the gold and silver caskets.
A director, though, could choose to have this done any way he or she wants. I believe the film version with Al Pacino as Shylock has three keys and Bassanio also has to use a key to unlock the lead casket.