Is there any way to find out how many groups are using a certain character sheet?

I created the Continuum sheet for someone else on the site, and it could use some work, the issue is, the changes would break a large part of the sheet(that is arguably already sorta broken as it is unwieldy and slow to the point that it isn't being used much by the person who commissioned it). I wouldn't want to break it for anyone else who is happy with the way it works now though... Should I just add the new section/way of doing it, and a note at the top that the old section will be removed at a later date, so the data should be copied over to the new section?

Unfortunately, there's no way of knowing how many people are using something. The approach you propose is how I've seen it done in the past and would likely handle it myself if/when I have sheet breaking situation arise.