When Sylvia and Janice were signing the form, they were in Apartment 22, which doesn't make sense since in theory Sam and Cat should get permission to enter their apartment after they got permission to use "Sam and Cat".
Sam had a banana in her hand for the whole time, even after she walks to the door. When the policeman wanted to take out his tazer, she had the tazer instead of the banana, but she didn't have a chance to touch the policeman's tazer.
Using a name similar to another one isn't illegal instead Sam and Cat would be hit with a lawsuit for copyright infringement.