Re: Mukachevo area births, 1871-1880 #records
Until about a month ago, was a Ukrainian genealogist named Alex Krakovsky who uploaded scans of every page of entire record books onto the Ukrainian wikipedia page for "shtetl". His lists of records violated wikipedia's standards and they were taken down, but if you go to an old version of the page, the list is still there with all the scans. It's not indexed, but you can use google translate in the browser to check what each record means.
Here's a link for the old version of the wikipedia page with the scans:
Coincidentally, I have Haberman in my family tree from the Mukachevo area (the village of Kalnik) and have a bunch of records already saved. Maybe let me know what you're looking for and I can save you some time.