At least some of the incidents cited in the OP were, in my opinion, deliberately intended to be humorous, including:
- "Scotty hitting his head on a low-hanging pipe"
- "Rom pouring liquid into his ear to treat an infection"
- "Picard suffering from temporal psychosis"
In the unintentionally humorous category, I would add, all from TFF:
- Kirk's fall off of El Capitan,
- the raising of the barricade when shuttlecraft Galileo executes emergency landing plan B as in barricade,
- the levitation boot ride up the turboshaft past the two deck 52's and deck 78,
except that in all of those scenes, I actually wanted to cry.