That's odd to hear. I also use Firefox and I've not had any issues. Are you just tapping to jump, or are you holding? Jump height changes based on how long you hold it. (This is assuming you've talking about the very beginning of the game. If you're referring to a different part of the game, it may be another issue.)
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Oh, I see. I was using the arrow keys, though up arrow does not appear to change jump height by holding it down like spacebar does.
After playing it, I think it was well done. The mechanics at the end were interesting too. I did find one spot I kept falling back past the previous checkpoint where there wasn't a barrier. Cool game!