Peter claims that the Giants are his favorite baseball team. In earlier episodes of the series he has worn both Yankees and Mets caps and has claimed that the Mets were his favorite team.
When Slimer goes into the lab room with the machine to explain what happened with the book, the door is shown to be both opened and closed. The Ghostbusters open the door a few seconds later on the already-opened door.
When Janine runs out to meet Ecto-1, the wheels of the cars are almost completely visible, but Janine's legs are not, making it appear as if she's standing in a ditch (this is so she can speak to the Ghostbusters at eye-level).
After Peter says "Okay guys, time to earn the big bucks", as he and Ray move forward, in the close-up shot Ray has no head or neck.