Critical Research Failure: In the first game, the description for the "Too Much Contra" achievement, obtained from entering the Konami Code, calls it "the level select code from Contra". Putting the Konami Code into Contra gives you thirty lives - it doesn't let you select a level.
Ear Worm - Before you complete or give up, the mellow but persistent trumpeting will infect your skull.
It only gets better with the piano music in the second game.
Good Bad Bugs: In Achievement Unlocked 3, the hamster gun shoots hamsters than can clip through walls, highlighting blocks that would be otherwise unreachable.
That One Achievement: Disrespect the dead #3. You have to jump on a corpse on the treadmill. After you commit suicide to get the corpse, you have two seconds to jump on it before it rolls off the treadmill, tempting abuse of the suicide button to spawn multiple corpses.