who made some mistakes in this context?
Solution 1:
Macmillan Dictionary defines "there must be some mistake" as:
used for saying that you think something is not correct or that you are being wrongly accused of something
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So, Muffy is saying that she thinks she spelled every word correctly and should be one of the representatives for the spellathon. She's objecting to the implicit claim that she misspelled or skipped a word.