Revealing mistake: In the part it shows Ash getting sucked into the time portal you can see the wire he is hanging from. (00:02:45)
Revealing mistake: In the windmill, Ash slips and flips into a handstand. The harness can be seen pulling away from his butt. (00:33:50)
Revealing mistake: When Ash is in the pit and the Wise One tosses him his chainsaw, as the chainsaw is tumbling through the air the ripcord on it is always hanging down. Shouldn't it be flying all over the place? (00:13:55)
Revealing mistake: In the pit, Ash uses his chainsaw to cut off the second monster's hand. In the shot from above where the hand is going up, the monster still has both of his hands.
Revealing mistake: When Duke Henry's soldier is thrown into the pit, the pair of soldiers holding him stop just short of actually throwing him off the ramp and he very obviously jumps into the pit. (00:09:55)
Revealing mistake: When Ash is forced to swallow one of the mini-Ashes, it's obvious that the two mini-Ashes pinching his nose aren't actually touching him and have been green-screened in. (00:31:05)
Answer: Towards the end of the film, when Ash mounts his horse and rides off into the sunset (before it then cuts to present day and he's back at the S-Mart), you can see his chainsaw is strapped to the horse's saddle. It seems that he either recovered it after the battle or perhaps he sent someone to the windmill to retrieve it.