It's fine if you didn't believe these things even though they happened to be in-character and easily explainable from context.
Only if the characters were supposed to be stupid, and you'll have to forgive me for being an "elitist" but I prefer it when my heroes are intelligent and do smart things.
Kirk's never been one to sit tight and wait for rescue when ordered to.
That does not excuse stupidity. I'm sorry, but when you are trapped on a frozen planet and you are warned of extreme danger outside you should not go outside. Kirk deserved to be eaten alive by that monster and that should have been the end of the movie. Stupidity leads to death; now there's a message I can get behind.
And that justifies promoting a cadet who was removed from active service and illegally stowed away on the the military flagship to first officer? Can you name precedent in the real world of anybody doing something as moronic as that? Pike is as stupid as Kirk, it's another case of the shouldadieds.
Your suspension of disbelief is broken, you should probably get it looked at.
On the contrary my suspension of disbelief meter is working perfectly, that's why I don't complain about the red matter, and my bullshit meter is finely tuned. I think you'll need to go get your bullshit meter checked because you seem to have bought a boat-load of it.
Every time I see someone write "turn off my/your brain" they seem to go on to harp on points of unrealism (you know, the stuff that demands suspension of disbelief) about the film like those above, which don't even really demand all that much suspension.
We've already been through this, suspension of disbelief != turn off brain.