If I had to pick one, I'd choose to not include an edit button. If a student needs to make a correction, they can always do so in the form of an additional response.

I believe it's a catch 22. On one hand, you have students that will use the edit option to make small corrections. On the other hand, you may open a gate for cheating. Students would now have the opportunity to change their response entirely. This might become an issue where institutions grade students based on the quality of their response where it's time sensitive.

Should students be allowed to edit their response on a discussion board once it has been submitted?