The Little League World Series uses instant replay. Each manager is allowed two challenges a game.
If they challenge a call and are wrong, they have one challenge left. If they are right, they still have two left.
The umpires will also use instant replay if there's a question among themselves as to a call.
As already mentioned, the replay doesn't take any longer than an argument.
Last year I was watching a game and if I remember correctly the batter got hit by the ball and was not given the base. The manager challenge and the play was overturn. I went back and time the play and it only took about 54 seconds from the time the batter got hit to the overturn of the play.