Most pronouncers are extremely skilled and know what they're doing. Surprisingly (or maybe not), though, there are many pronouncers (especially at more local spelling bees) that pronounce a few (or several, or most) words incorrectly. If you've participated in a good number of spelling bees, you've probably been there. The pronouncer says your word indecipherably wrong, and you spell it wrong as a result. (I've definitely had my share of these experiences as a speller). When you try to appeal due to the mispronunciation, the pronouncer and judges refuse to hear your case, insisting they pronounced the word correctly. It's not fun for anyone involved.
Fortunately, there are a few things you can do to prevent getting into this situation beforehand. If you know that the pronouncer at a certain bee is sometimes less than competent, then, as backwards as it may sound, have someone quiz you on the words you're studying while intentionally mispronouncing them in a number of ways so you can get used to deciphering incorrect pronunciations. Come up with ways--yes, even absurd ones--that a word might be mispronounced. It may seem odd, but it could save you from elimination as a result of mispronunciation.
That being said, it could still happen. If you're anticipating mispronunciations, print out the pronunciation guide on Merriam-Webster Unabridged and take it with you just in case you have to appeal. That way, you'll have concrete evidence regarding diacritics with which to argue your case. You've worked too hard to be eliminated by a mispronunciation--it's better to appeal and risk being eliminated anyway than to not try at all.