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So, at one of the schools I applied to I submitted a personal statement with a few grammatical errors and a small formatting issue. Basically, I lost access to Word and O had to transfer everything to OpenOffice. I accidentally transferred a older version of my personal statement.

I wasn’t going to say anything, but there was more than one mistake. I emailed admissions, explained what happened and apologized. I also asked if it would be advisable to submit the updated document. I have yet to receive an answer and it’s been two days.

I know it’s really busy, but did I just destroy my chances? I am a splitter.

Highly unlikely. Schools really only care about your LSAT and GPA so if they need whichever one of yours in attractive to them they will likely admit you. Everything else is just fluff which really is only considered if yours is truly terrible or they are trying to decide between two candidates and everything else is similar. I doubt minor grammatical errors will have any impact, especially if you explained the situation. I wouldn't worry about them not responding right away either. Like you said they are likely very busy and this is not a priority to them.