There are a lot to choose from, like 'The Core', where Aaron Ackheart travels to the center of the earth in a tube made of unobtainium to detonate nukes to restart the earth's core. In this movie's defense, it REALLY didn't take itself seriously.
No, maybe not the worst example, but the one that sticks out most in my mind, is 'The Day After Tomorrow'. Same premise as the OP's movie shipwreck, kind of, with 'super scientist' versus 'lazy polititian', and the world's coming to an end. Okay, it's a movie about global warming. I can deal with that. I'm not really on board with the whole global warming thing (mainly that part where we caused it), but whatever. What I really have trouble with is the storm fronts they have. There are these super hurricanes with miles-long eyes that are funneling super-cooled air from the stratosphere and instantly freezes everything it touches. I barely know where to begin. First off, this kind of funnel would be impossible unless the pressure inside the eye, and below it, were much less than the pressure of air in the stratosphere, as to say, negative numbers lower. Thus, no one would have been alive. Since everyone was alive, pressure must have been at normal levels, which brings me to my second point. Air that high is super-heated by the sun, it just feels colder because it's so much thinner. Kind of. Well, in thermodynamics, heat is particle vibration and pressure. Lower the pressure, you lower the temperature. If you take a bag of air from 50,000 feet at 0 Celsius, and bring it, within a few seconds, to ground level, the pressure now on that bag with the vibration of the particles would bring the air in the bag up to 50 Celsius. Easily. That air wouldn't have been super-cooled, it would have been super heated, and melted the ice instantly.
I was very disappointed that not everyone in the movie died.