The night the Corbetts are moving out of their old home to go to the one that Jim had bought for them, the shadow of the boom mic is clearly seen moving along the left wall as they come down the outside steps.
In the fight scene at the beginning of the movie, when the police swarm in and begin beating the two fighters with their night sticks, you can clearly see several of them flexing as they are being swung. This is particularly evident with the officer on the left as he repeatedly hits "The Mauler". It's obvious they are made of rubber.
In the bank the day after the first fight (and their arrest with the bank director for attending it), Corbett (Flynn) and Lowrie (Carson) decide they should resign preemptively, rather than wait to be fired. However, Corbett gets a raise instead and returns from his boss's office to tell his pal Lowrie about it. As he talks, he's counting a stack of "money" of which only the top and bottom sheets appear genuine. The other "notes" are all blank sheets of paper.