When showing the exterior of the Pawtucket Brewery, you can see the initials of the company, "PB," over the front gate; however, just before Peter is informed that he will be going to prison for blowing up the children's hospital, the gate only has a "P" on it.
When Peter goes to court for blowing up the Childrens Hospital, you will see the American Flag to the judge's right and a blue flag to his left. The state flag of Rhode Island isn't blue, it has a white background with an anchor in the middle saying "Hope".
A tiny blow torch cannot generate enough heat to lift a hot air balloon and a house.
In the "bum rap" cutaway, Abraham Lincoln gets a cell-phone call from someone who is implied to be Thomas Jefferson. While the anachronism of a cell phone in the Civil War can be ignored as humorously deliberate, Lincoln can't have been talking to Jefferson; by April of 1865, when Lincoln was assassinated, Jefferson had been dead for nearly 40 years.
It makes no sense that Peter can just walk into the executive bathroom without the key and without being challenged.
It makes no sense for Peter to get motivated to become an executive for the bathroom privileges since apparently they are not enforced anyway and he can just use it without actually being an executive.