I agree with the "How are you" issue. Not a pet peeve, exactly, but it is annoying when it's insincere. Just say "Hello" or something else unless you really want to hear with some level of detail about how things are going for me.

I guess the things that come to mind for me are common grammar errors, like choosing the wrong option from your/you're, their/there/they're, base/bass, and to/too. It's/its is a little trickier, so I don't get as annoyed at those errors. But for the record, use the apostrophe for "It is", e.g. "It's too bad Michael has hemmorhoids," but not for the possessive, "The Preparation H has lost its potency."

I also can't help but notice certain misspelled words, e.g. separate. Remember, there's "a rat" in separate.

Bears, beets, Battlestar Galactica.