The length of Penguins cigarette ash in the umbrella shop keeps changing.
When Batman and Robin enter the umbrella factory, Robin enters first and Batman follows. In the following shot, Batman is seen entering first with Robin behind.
The length of Penguins ash in the umbrella shop.
As a duly deputized officer of the law, Batman's placing of a bug in the Penguin's shop would be illegal in itself, and any information obtained from, through, or as a result of it would be inadmissible at trial as "fruit of the poisonous tree." Batman should know this, and his unwavering moral code ought to prevent him from even considering it.
Even the most inept jail would not allow an umbrella into a jail cell.
When Batman puts the faulty umbrellas under the asbestos blanket and they begin going off, a wire can be seen holding the blanket.
The camera angle in Penguin's cell changes repeatedly, even though the camera itself is stationary.
The "quacking" penguin alarm in the umbrella factory has a wire opening/closing its beak.
A close-up of the rear of the bat car you can clearly see a pair of parachutes they use as a breaking mechanism. As they drive out of the bat cave the parachutes are no longer there.
Even if he was scheduled to be released shortly, prison officials would never allow Pequin's cellmate to wear a mask partially concealing his face.
In the bank, Batman tells the police officers to place the umbrellas in the wire basket behind the table, but he could not have seen the basket from where he was standing at the front of the bank.