The announcer during the Star Trek-style opening sequence mentions that Christmas is Jesus Christ's birthday and that of Dean Cameron, who played Chainsaw in Summer School (1987), This is all true, Summer School's Chainsaw was born Christmas 1962.
When the Cobra characters are singing Deck The Halls in the Cobra Carols clip, the camera pulls back to show a character "stuck" on the "La La" part of the lyrics. This is Golobulus, who was the primary antagonist in G.I. Joe: The Movie (1987), leader of an ancient civilization called Cobra-La. In reference to him and Cobra-La, in the movie Serpentor changed his war cry from the usual "Cobra!" to "Cobra La-la-la-la-la-la-la-la-la".