If you don't catch them, many do it all the time, so can they, of course,

Now do you want to know if it is illegal and if they do, you can sue them for money back ? If that is your question, yes, they are not legally allowed to collect rent from two people on the same property during the same time.
*** not talking about multi family rental but the same apartment after one moves out, and they find a new renter

There is a difference between the meanings of the words CAN and MAY. Too often they are used interchangeably when they shouldn't be.

As Chuck said, its illegal in Florida. BUT, you have to be sure that double dipping is occurring. For example, there may have been an early termination clause or settlement on a lease. So lets say, a lease expires 6/1/11. In October, the tenant goes to the landlord and says they need to move out by 12/1/10. The landlord negotiates a buyout (or there is a clause in the lease) of 2 months rental. So the tenant pays for Nov, then gives the landlord 2 months rental as the early termination penalty. The landlord, in the meantime, finds a tenant who moves in on 12/1. This would NOT be double dipping.