Believe it or not, Star Trek II was filmed on a budget. That meant they didn't always have the money for high-end effects. Luckily, they already had plenty of effects shots from the first film…and with some judicious editing, hardly anyone noticed. All of the effects shots of the Enterprise leaving space dock and heading into the cosmos were actually from Star Trek: the Motion Picture, recycled for use here. The VCR was still pretty novel, and most people likely hadn't seen The Motion Picture in years. That made it pretty easy to perform a little sleight of hand and shave a few million dollars off of that budget. (Source)

Poor Chekov gets that space eel stuck in his ear after a tense reunion with Khan in the Botany Bay…but in fact, it's not really a reunion. The original Star Trek episode with Khan, "Space Seed," took place in the show's first season. Walter Koenig didn't start working on the show until the second season…meaning that we never see Khan interact with Chekov in the original episode and Chekov doesn't even appear. Of course, there's nothing to say that Khan didn't run into Chekov somewhere on the Enterprise (maybe they grabbed some coffee in the rec room or something), but it's odd to note that they didn't seem to have any past before the whole ear-worms thing made it complicated. (Source)

Paul Winfield, who plays the ill-fated Captain Terrell here, wasn't done with Star Trek, despite his character phasering himself instead of letting the ear-worm chew on his brain. Nine years later, he appeared as Captain Dathon in an episode of Star Trek: The Next Generation entitled "Darmok." (His character belongs to an alien species who speaks only in metaphor, which we think is the coolest thing in the universe.) The episode is widely considered one of the best The Next Generation ever produced, leaving Winfield with a pair of wins in his Star Trek column. (Source)