I make edits for questions where the sentence syntax is just really bad. Since I don't have editing privileges, the system says that my edit will be "peer reviewed". Does this really happen, or should I not bother?
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Edits normally get peer reviewed quickly (especially if it is a newer question).
Go ahead and keep submitting edits when you find these cases.
Look at this link at the bottom to see that you have 4 edits approved:
Yes: by all means, please do - the amount of posts that needs editing is overwhelming. Usual editing recommendations apply: keep the author's intent, and edit if it improves the post substantially (which is often the case with lolcat-grammar-posts).
When you do that, people with full edit privileges (currently 2000+, IIRC) can approve or reject your edit - with this being a global site, this usually happens within minutes.
For the complete explanation, see the SO blog: http://blog.stackoverflow.com/2011/02/suggested-edits-and-edit-review/
As long as you do a thorough job and clean up all the spelling and grammar mistakes then your edits should be approved OK. Don't forget the title either!
It's where people just reformat code, or correct a couple of spelling mistakes and leave other (potentially more serious) problems untouched where you will find edits being rejected.