I love sci-fi. I even love bad sci-fi, but I have to admit that even some of my favorite sci-movies can be pretty stupid, particularly give the fact I'm a physicist, so things bother me that wouldn't bother other people. Kind of like doctors and nurses can find fault with medical shows that seem just fine to me.
A list of everything stupid and unscientific in science fiction movies would get really long, so I'm going to restrit myself to a list of movies with the most ridiculous fundamental premises:
Silent Running (1972)
OK, let's get this one out of the way first, because the fact is I loved this movie. After all, it's got Bruce Dern on a spaceship. What more could you want? The problem is it's based on a really dumb idea; namely, the Earth's environment has gotten so bad they launched a bunch of bio-domes into space with little forests in them - and not just into orbit, but into interplanetary space. Now you don't have to give it too much thought to realize that no matter how hostile the environment on Earth is, it can't be as bad as space, so it would have made a lot more sense to build those little domes on the ground.
But then you wouldn't have a movie.
The Matrix (1999)
This one is going to make some people angry, because some people are crazy into The Matrix. The fact is that the idea that we're all living in a world of virtual reality is actually kind of cool. The problem comes when they tried to cook up a reason it was happening. Using humans as a power source doesn't make any sense at all. Even if you ignore the fact it violates the laws of physics - it takes more energy to keep a body alive than you can extract from it - they never come up with a reason you'd need to invent a complex virtual reality for them. Just knock them out and keep them alive. If you think for a few minutes, you can come up with a whole list of more plausible motivations: using humans as a big computer, experimenting on them, etc. Pretty much anything is more believable than what they came up with.
This is an obscure one, but it's probably got the dumbest premise of any sci-fi movie I've ever seen. After series of natural and man-made disaster, there's a very strong wind that blows down a canyon. People use it to fly gliders, but only in one direction. Really, that's it. That's the premise. The funny thing is that in spite of this completely nonsensical motivation, it's actually kind of a cool movie. As they travel from place to place, the main characters encounter weird remnants of civilization. Even though it never really goes anywhere, the atmosphere is kind of cool. Also, one of the few post-Star Wars roles for Mark Hamil. There's even a cameo by Ben Kingsley.
A mad scientist dreams of combining man with fish. It's never clear why this is a good idea. No redeeming qualities. It's just a terrible movie from beginning to end.