Good question.
With the way the law school application process works your applications will not be reviewed until they are complete with all the required bits and pieces in place. That means that none of the admission committees will review or consider your application until everything has been received by LSAC and processed into your CAS (formerly known as LSDAS) file including an LSAT score.
Since you will not have a reported LSAT score to make your applications complete and ready to review until the end of December you now have more time to further polish up the pieces of your application you still have control over, meaning your personal statement, any addenda you want to include and your LSAT score.
Double check and submit everything else as soon as you can, including your LOR's, transcripts, required personal/biographical info etc. to get it all processed into your file so all that remains for your application to be 'complete' is your personal statement, any addenda and your LSAT score. Then use the extra buffer time you have to again review and make sure your personal statement is the best it can be.
I've found that when people re-read what they wrote and decided was the best final draft of their personal statement several weeks or longer after completing it they have a fresh perspective and notice additional ways it could be improved they didn't see before. I had two glaring typos and some awkward sentences in my personal statement that I did not notice until I decided to re-read it while waiting for admission decisions even though the version I submitted was my 10th major draft and I had proof read the thing countless times before submitting it!
With the online electronic application submission process it does not take long for your personal statement and addenda to get processed into your file once you submit them.

Couldn't've said it better myself.
