Use featureclasses in a file geodatabase and I see no reason to keep updating one file repeatedly especially when you seem to keeping old boundaries mixed in with the new. If you aren't using topology, there is little you can do to meaningfully clean up the data. How and by whom is the data being updated? and are all the apparent changes realistic? (roads and building boundaries that suddenly change suggest data management/processing issues)
thank you for taking the time to reply to this! The data was originally collected by the state from 2011 precinct boundaries, and is being updated on a county level to reflect more recent districting. All apparent changes are realistic, but they are sometimes off by a few hundred feet or so compared to the original 2011 data, thus creating the appearance of a new polygon from lines that aren't correctly matching up.
off by a few hundred... sounds like a datum shift (eg NAD27 vs NAD83 or whatever is appropriate to your area).
I would check those very carefully, make copies and get all the copies into a common/current coordinate system using the Project tool with an appropriate datum transformation.