When Boromir goes to the door of Balin's Tomb in the mines, you can see Aragorn in the background putting his torch on the ground. Then, when it switches to Aragorn and the others, he puts the torch down again.
Aragorn is handed Boromir's torch, which he then puts down. Later, he see he won't need his torch because of the light coming into the chamber and puts that one down so as to have both hands free to wield his sword.
I never saw Boromir holding a torch in Balin's Tomb, nor did I see anyone hand Aragorn a second torch. He does indeed put down a flaming torch as Boromir closes the door, then puts down another flaming one in the same way two seconds later, in the same spot. If it was Boromir's torch, wouldn't there be two torches on the ground now?
Not only that, but you can see Gandalf usher the Hobbits behind him twice, once when Aragorn puts the torch down for the first time and a second time after Aragorn yells to them to stay close to Gandalf. Maybe this wasn't a slipup, but a second of rewinding and showing the same thing again from a different angle?
this is very good spotting. after putting down the torch aragorn then starts to pull out his sword... then after boromir almost gets hit by orc arrows you aragorn again WITH a torch and no sword out... it helps if you have a slow- mo thing