At the beginning, when Phelps is listening to the recording, the tone arm is near the middle of the record. When the message is finished, it's then near the outside edge of the record, the opposite of where it should have been.
When Phelps drops the needle on the phonograph recording, the first shot has him using his left hand; the second his right hand.
Near the end, when the hoods leave the apartment, going back to their car. Johnny, who had been in green overalls to rescue his boss, has suddenly gone back to wearing his suit.
As Jim plays the mission statement, he places the player arm in the middle of the recording. During the playing of the statement, several shots show the arm first moving in toward the center, then back to the outside - an impossibility. Records always play from the outside toward the center.
When the team starts digging up Jimmy, they insert an aerator near his head. This wouldn't do any good. There's so much dirt on top of him that he wouldn't be able to inhale as his chest would be unable to expand.
When Phelps asks Dr. Reese how much time they have before they must dig Jimmy up, he responds, "We better get to him in two and a half minutes at most", however his lips clearly say, "...two minutes and a half minutes at least."
The police would question why Frank has a mask of Rollin. The media would likely find out about the mystery and print Frank's face with the Rollin mask ( perhaps blowing Rollin's cover) for future missions.