Character mistake: Griffin states about the New York Mets saying "They were in last place every single season until they won it all". That is not true. They came last ever since they started in 1962 to 1967. In 1968, the year earlier, The New York Mets came second to last where as The Houston Astros came last.
Plot hole: When (future) Agent J and (future) Boris are fighting on top of the large red docking station for the spaceship, Agent J gets shot deliberately by Boris and jumps off the edge of the dock. Then he uses his time travel device to go back in time a few seconds earlier to be able to dodge the shots. There are a few mistakes in this part. 1) There should be another Agent J and Boris there too, as they have gone back in time to that moment again. However in the movie there are only two of them. 2) The injuries sustained by Agent J (the bone spikes in his abdomen) should have remained there when he went back in time. If it were true that you healed once you went back in time into the condition you were in at that moment, then Boris should have grown an arm back when he went back in time. 3) Due to the time loop, Agent J remembers how to dodge the shots, while Boris doesnt remember anything and is surprised by the outcome.