Before you start working at your correction email, think about the format and style of the message, what you will say in it and who will get it.
The format of the correction email depends on the type of the mistake you made in the original message. If the mistake was in the email itself, you can just resend the original email with the corrections made, but include a brief note at the beginning of the message and a subject line that refers to the correction. If the mistake is connected with your website (the page doesn’t open, the button doesn’t work, etc.), you can send a simple plain text email notifying people that the error or problem on your website is corrected.
Whether you resend the original email with an intro note, or prepare a separate correction email, the message should be concise and to the point. It should start with “We made a mistake”, or “Here is the fix”, or "The error is corrected" or something like this. You can also include a special offer for your subscribers when appropriate – “Here is an offer to make it up to you” – for example, an offer could be a free shipping, free access to an e-book, report, free download, discount for the next purchase, etc.
Lastly, think about whom you will send the correction email to. If you sent the original message to the whole list, send the correction email to all your subscribers too. If the email with a mistake was sent to a segment from your list, then it makes sense to resend the corrected email to that segment. In the case of website issues (now corrected), send the correction email only to the recipients who have either opened the original message or clicked on the affected links.