Forewarning: The following list is intended to be humorous, even to the majority of people who liked the movie. If you don't find it funny, it's just that my humour is crappy, not that I was bashing the movie (no matter what I think of it).
Oh, and this contains spoilers too.
- A single drop of red matter can destroy a sun or a planet, and create a black hole through time and space no one can escape from. A whole beach ball of it can destroy a starship and create a black hole, easily escaped from with a few explosions. Maybe a shipload of it would have created a pretty firework.
- There is no need for an universal translator, as the entire universe has learned to speak flawless English. Either that, or the universal translator has not been programmed to cope with russian accent.
- Cheating an exam and illegally boarding a starship is okay if you can subsequently identify a trap, and it will get you an acting first officer rank. Some nerds just bother themselves with graduating from Starfleet Academy and serving some time as enseigns...
- Nokia phones are still used in the 23rd century and still use the same ringtone. They probably have changed their motto to "Connecting lifeforms", though.
- When dealing with an unruly crewmember, drop him on the nearest monster-infested planet. If he survives, he can then be made captain. This is Starfleet implementation of Darwin theories.
- Vulcans being portrayed as self-righteous and intolerant jerks is completely okay, as long as it happens in a story Braga and Bermann had nothing to do with.
- Lighting storms are the telltale sign of a Romulan trap. And all this time we were fussing about detecting cloaking devices and scanning subspace transmissions...
- The destruction of a single ship is enough to alter the timeline so that 25 years later people invented transporters with a light-year range, made contact with the Romulans and Cardassians, and could reach Vulcan in a few hours at warp 4. Maybe Starfleet should implement destroying a few starships from time to time as a policy in order to jumpstart its development.
- There is no sound in space. Someone finally told them.
- Forget the holodeck, the Enterprise is now outfitted with a giant waterslide in engineering. Now we know how Scotty used the time he gained by exaggerating his repair times.