Corrected entry: In both scenes with the 'helicopter' umbrella, it shows simply the small spokes attached to the handle. Now, even if there were a motor small enough to drive the 'blades', its not spinning near fast enough, the 'blades' are nearly big enough to move any air, and the absence of a tail rotor would mean that anyone standing on the handle would be rotating the opposite direction as the blades.
Corrected entry: At one point, one of the Penguin's clowns kidnaps the mayor's baby, and drops into a sewer to hand the baby to The Penguin. As we peer into the sewer, we see that it's a narrow stone shaft. The Penguin then slowly emerges from the manhole from one of the ducks he keeps in the sewer. He would not have been able to emerge as far as he did even if he stood on the duck's head.
Corrected entry: When Selina returns home from work she takes milk out of the fridge and pours her cat some, leaving the carton on the bench. She then realises she forgot something and returns to the office. After being pushed out of the window, Selina returns home in a daze and gets the milk from the fridge to pour some for her cat. The milk was never put back in the fridge when she left her house the first time.