And we should proofread for not only grammar and punctuation, but also attachments. We’ve all sent emails forgetting to attach a document or picture that we announced was attached. How embarrassing is that? You certainly don't want to inquire about a job and forget to attach your résumé! A worthwhile practice is to insert the recipient’s email address only after proofreading the body of the email (including the subject line); for a reply email, merely delete the “.com” until you're ready to send the email. As for the attachment, just attach it before you even begin to write.
My advice is to slow down (just for a few minutes!) to give yourself time to proofread.