There were no FBI officers on the scene of Kennedy's assassination. The FBI did not become involved in the case until later in the day. A secret service man would have more likely been the one who would have found the Red Dwarf crew in the book depository.
When the FBI officers fire their guns into the box of books when the helmet disappears, the boxes aren't damaged which means the guns had only blanks.
The brick walls of the exterior of the book depository wobble when Oswald falls out of the window to his death and then again moments later when the Dwarfers slam into the window frame.
When the gunman is outside the window the ground can sometimes just about be seen at the bottom of the screen. They are supposed to be a few floors up, as seen in other shots.
The brickwork on the walls inside the book depository is quite obviously painted on.