One bit of unexpected humor was in "Terra Prime" where Reed is on the shuttle, and making comments about his stomach coming up (due to turbulence). Doctor Phlox makes a comment about having something that will help, but Reed tells him that Phlox has given him all the medicine that Reed can handle. Doctor Phlox merely hands him a barf bag.
Just a simple item, but it was well placed. No fancy pills that instant cure, even the medicine can reach its limits, but good old basics work just fine.
Edit (added stuff):
Plus the comment from one of the ambassadors, "There are protesters chanting outside the Andorian embassy... and they're using words that aren't in the universal translator."