As far as I understand there are set of "common" reasons for edits, such as correction of spelling, correction of grammar, format improvements etc. If we can show a small form of most common fixes along with a field to enter any custom text, most users will tend to provide an input on this. If you are not lazy to fill the text box you can still use the custom text field along with the tick boxes.
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I would not favour tick boxes because it would waste space. Also, I like to use TAB to navigate to the submit button and this would made it longer to reach it.
However I would be in favour of a dropdown list of “canned comments” for example. Maybe also using Ctrl-K or CTRL-Q could autofill the comment box if it is empty with comments such as “formatted code” or “formatted quotation”.
There might already be a Greasemonkey script to do something like that on StackApps but I could not find a relevant one in this list. Please improve my answer if anybody can find it.