Trivia: As per the documentary "Never Surrender": The ships designation "NTE" stands for "Not The Enterprise" and was chose to avoid (or defend against) copyright issues that might have been raised by the owners of the rights to the Star Trek franchise.
Trivia: The film was originally going to be directed by Harold Ramis, but he stepped down due to creative differences with the casting.
Trivia: Tim Allen wasn't the original choice for Jason Nesmith. The producers and original director wanted Kevin Kline to star in the film as Jason, but he turned it down. Reportedly, Alec Baldwin loved the script and campaigned aggressively for the role and was also considered, but ultimately wasn't chosen.
Trivia: When the captain and Gwen enter the room to disengage the core overload Gwen's shirt is slightly open, then a few seconds later it is ripped down so you can see her bra. In a deleted scene she was showing her boobs to the two bad guys.
Answer: There didn't seem to be any special f/x that were in the trailer that weren't included in the film itself. The only shots that were certainly not in the film was the opening shot that shows the aliens watching one of the Galaxy quest shows and when the narrator introduces Sigourney Weaver where she is showing off her chest (which is a deleted scene on the DVD). Your explanation of why they are not there is the most likely reason they were cut.
Lummie ★