Does all bad science in films annoy me? No. When Star Wars spacecraft handle (and sometimes sound) like planes with piston engines, no problem, because Star Wars is unashamedly a fairy tale in SciFi clothes. When a damsel in distress falls 200 feet down a skyscraper and hits a Man of Steel coming the other way, of course she is going to be fine because momentum works differently in superhero movies. As Any Fule Kno. In fact the above aren’t bad science, they suit the film.
What annoys me is the gap between how serious/scientific a film is pretending to be and how it is, otherwise known as “Sunshine syndrome.” If you boast about your scientific advisors and then make a schoolboy error like confusing air pressure and gravity, then you deserve ridicule. And having to do an Olympic opening ceremony to make things right.
A lesser annoyance is when something could very easily be made credible without disturbing the rest of the film, but isn’t. Take the Matrix movies, and the machines using humans for power. You don’t get more energy out of a system than you put in, of course. It would have made more sense if the machines were using the brains for processing power, or to sample human emotions. Wouldn’t have altered the film except I wouldn’t have winced at that point.
Or (plot example) the start of The Dark Knight Rises: how come the pilots didn’t notice a massive transport plane on their radar flying up behind them, or try evasive action when attackers abseiled down? Why were they flying so slow that this could happen in the first place (to film it, they needed an unusually slow-flying aircraft to make the stunts possible). Naturally, the pilots must have been IN ON IT. Would only have taken a second of film to establish that!