Continuity mistake: When Bruce wakes up after getting shot in the head by Two-Face, there is a "BW" (Bruce Wayne) on his pillow next to his left ear. But after Alfred asks, "How are you, young man?", the "BW" is gone. (01:35:55)
Continuity mistake: While retrieving the safe from the chopper, Batman tells the bank guard to "hang on." The guard holds on to the chain to which the safe is attached. But as the safe comes back into the vault, the bank guard is holding on to one of the tubular structures of the safe itself. (00:09:35)
Plot hole: In the scene at Wayne Manor where they show Harvey "Twoface" getting scarred with the acid on TV, you can see the acid cover almost his entire face before he puts the folder over to protect it. (00:24:15)
Other mistake: The shot showing the vault swinging back to his location is the same that the one where the vault is swinging out, but going backwards.
Continuity mistake: After causing Two-Face to accidentally blow up a car that had a couple members of his gang in it, with his missile-launcher, Batman speeds by Two-Face with the Batmobile as he is being chased by other members of Two-Face's gang. In one shot the Batmobile is very close to Two-Face, but in the next shot the Batmobile is far away from Two-Face (when he tries to throw his missile-launcher at the Batmobile). (00:49:05)
Continuity mistake: In the fight scene outside the elevator at the beginning of the movie, there are at least two shots where you see Batman's back without his cape in the way. There are no items whatsoever attached to the back of his belt. Subsequently he manages to pull the stun device and the grappling gun with grappling hook from behind his costume. A previous corrector proposed that the devices could not be seen because they are concealed in "pouches" on Batman's belt. Close inspection of the scene shows that there are no pouches of any kind on his back or concealed in his cape.
Continuity mistake: When Bruce is at Dr. Meridians place, Bruce receives a call from Alfred. Bruce moves his finger on the side of the communication device up. The next shot shows him doing it again. (01:02:05)
Continuity mistake: Two-Face and the Riddler are in Two-Face's lair; the Riddler has just said, "Then I taught my doggie a new trick; how to map the human mind." In the establishing shot, the tube is in left hand; after the cut, it's in his right hand.
Revealing mistake: When Batman is hanging from the chain that is connected to Two-Face's helicopter, you can see a dark area at the bottom of the screen. The dark area is a shadow, and you can tell it's green screen. And yes I know he's hanging off a helicopter.
Continuity mistake: After the Bat-Boat is destroyed, it changes to a normal wooden boat. (01:41:50)
Continuity mistake: When Dick Grayson is showing off his fancy laundry skills, he splashes water onto the washing machine and dryer. In the last shot when he mops up the mess, the water is gone from one side of the machines.
Continuity mistake: In the dream/memory where young Bruce is falling into the cave, the red book is in his right hand as he starts to fall. It is dark and raining. The next shot shows him at the top of the hole falling and he has dropped the red book. It is also bright outside with no signs of rain. The next shot shows him with the red book in his left hand. When he stands the book is in front of him, too far away if he held it. (01:30:00)
Continuity mistake: When Bruce slides across the table, both pumpkins go the right near Dr. Chase. In the next shot, they are on each side of the table. (01:32:55)
Continuity mistake: When Edward Nygma is in his apartment after killing Stickley, we see him pasting letters for the next riddle involving the match head. However, when Bruce and Chase are in her office looking at the riddle after it was delivered, you can see the letters are in different positions than the earlier shot.
Continuity mistake: Bruce's hair is much flatter and messier in the garage than in the previous scene outside when Dick is leaving, even though the garage scene happens directly after.
Other mistake: When Batman puts the lit torch to the cable and the cable breaks; the vault goes back into exactly the same place where the helicopter lifted it out from; connected via a grapple that Batman put through the wall. Ignoring the logistics of how this would be possible, it tightens the grapple, which surely, with the weight of the vault, would have ripped itself away from the wall.
Continuity mistake: In the beginning Batman suits up with a heavy leather-like cape. When he swings to the street his cape flaps and ruffles in the wind like thin silk; very obviously a completely different material.
Revealing mistake: When Dr. Meridian first drops out of the tube, her skirt flies up. However, when she is falling in the shaft, her skirt is down and barely moving. (01:46:55)
Continuity mistake: During Bruce's first session with Dr. Chase, when the two are talking about the dream doll, she puts a jacket on. The way the hood lies on her left shoulder changes in every shot. Sometimes, the white part covers her shoulder, sometimes it doesn't. (00:31:20)
Continuity mistake: In the vault, just before Batman enters, we get a nice shot of the bank guard. He appears to be lying length-wise in the vault, his body flat and straight, and his head laying on the "step" toward the left side of the screen. When the scene cuts to Batman entering the vault, the guard is positioned differently, at much more of an angle, and his head is higher, closer to the second row of boxes from the bottom of the vault. (00:07:25)
Chosen answer: Batman talks like that because if he talks like Bruce Wayne (Val Kilmer's voice) his voice might be recognized, leading to Batman's identity being revealed.