In his first appearance, Allan A. Dale claims to be the Wayne Foundation's administrative head of public relations. Later, he claims to be in charge of the foundation's money. The person in charge of a foundation's money is its treasurer, who answers to the president or executive director, who ultimately answers to the board. The head of public relations would not be in the financial chain of command at all.
Allan A. Dale claims that the $10,000,000 in will come direct from the U.S. Mint in crisp new $100 bills. This is impossible: The U.S. Mint is only responsible for minting coins. The printing of paper money is the purview of the Bureau of Engraving & Printing, at the direction of the Federal Reserve.
When the Archer's henchman shoots an arrow that curves around a corner, the arrow leaves the bow without the bowstring having been released to fire the arrow.
At 3:14 when Batman and Robin use the Bat Springs, you can see the wires that pull them up in the air.
Alfred, dressed as Batman and using his 'voice imitator' comes up with the excuse (to not come close to Com. Gordon) that he has a contagious cold. That accuse doesn't withstand as Gordon had seen him, standing close to Robin.