Funny enough, going frame by frame during the Enterprise warping scene, she seems to leave a pair of "trails" behind her warp engines like the Enterprise did in some of the movies.
Also, you can barely hear the edit, but the line "Do you have any idea what a pain you are" sounds cut. Probably couldn't get away with calling Kirk a pain in the ass on what is meant to be a "kid-friendly" trailer.
Also, I love Spock's line after the ship Kirk is flying barely manages to not get smashed. "I am not sure that qualifies." Dead-pan snarkiness from our favorite Vulcan.