Revealing mistake: When the Federation fleet is preparing to warp to Vulcan, you'll see the first ship blast off, but the second ship blasts off out of nowhere. You could argue that the ship was out of sight and below the Enterprise, but the light trail isn't that long. The light trail starts in front of the Enterprise where you should be able to see a star-ship. (00:40:45)
Revealing mistake: At the end of the film, when Kirk is receiving his medal, in the background you can see the female alien crewmember from the Enterprise bridge clapping with very human-like hands. (01:56:15)
Chosen answer: Phasers fire nadion particle bursts or bolts, which are fictional but are presumably similar to photons, and would therefore have mass and kinetic energy - so depending on the power output of the phaser, it should impart a not insignificant momentum change.
Sierra1 ★