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None.
Very mild, mostly on the sequence based aboard the carrier Enterprise. The character "Chekov" is chased through corridors by armed Marines ready to fire. Chekov falls off the ship and is gravely injured (though later is seen to be healed by the character "Dr. McCoy"). The character "Mr. Spock" administers a nerve-deadening pinch to render a punk on a bus unconscious as the punchline of a gag sequence.
Many, as the characters call them, "colorful metaphors" are thrown about for humor. All are mild and on the order of "double dumbass on you!"During a scene with a punk on a MUNI bus, a punk throws the middle finger when asked politely by the character "Admiral Kirk" to turn his radio off.
Some social drinking of beer.
The time travel scene may be somewhat unsettling for small children.