Just before the DeLorean crashes through the Courthouse clock as it leaves 2015, look carefully at the clock and you will notice that it is actually working and displaying the same time as the time circuits (3:44am), even though this takes place merely a few days after the 2015 events of Back to the Future Part II (1989) and the clock was still not functional and stuck on 10:04pm in the movie.
Look closely at the security monitor when the dog is watching them and and see Biff is taunting the security cameras with a dog bone in his mouth. Likely this was used to get the dog to bark at the security monitor. Where he got the bone from and where he was keeping it is never seen. It's not seen in his mouth in the direct shots before and after the scene.
During one of the preflight videos Doc Brown mentions to the test subjects that Biff Tannen graduated Hill Valley High class of 1955. However, since Back to the Future clearly stated that he was still in school in November of 1955 the soonest he would have graduated was class of 1956.
In the movie Doc explains that the time destinations are input by a keypad by the year, date and time. The year only has 4 digits. The time machine is only capable of traveling from the years 0000 to 9999. Yet during The Ride the time machine gets transported back to Hill Valley 65 million years ago. There is no way the date can be imputed to travel back that far.
As you enter Hill Valley town square and approach the Courthouse, look down the alley to the right of the courthouse to see a giant styrofoam cup of coffee accidentally left on the miniature set.
At the end of the preflight video, on wide screen televisions the boom mic is visible toward the top left of the screen, next to Doc Brown.