Factual error: In all sequences where Maverick "puts on the brakes", he is shown pushing the throttle quadrant forward and pulling the stick back. This would put him in a full-afterburner climb, but you don't really stop and it doesn't work in a medium speed tail chase (which is easier to film). The air brake does effectively nothing on the F-14 because it is too small, and not deployable at full power.
Continuity mistake: Take notice of everyone's hands during the action sequences. No one is wearing gloves. As standard issue for military pilots, the gloves are made of Nomex and provide protection from fire and allow for a better grip when things get a little hot and heavy.