Lucky my theater used the 4K projector (which now runs both ads and films) instead of the old advertiser they used before converting to digital cinemas. I would have been annoyed watching from a advertiser projector, seeing the scan lines on the screen.
Hmm, that's odd your theater would use the expensive 4K projector to run ads, burning precious time on the more expensive lamp. Trailers, sure... but ads? I guess it's ultimately up to the theater, but that sounds really, really unnecessary. You're very lucky you saw TNG that way, though! From what I understand that's unusual. Fathom usually only exhibits on the advertising projector, which can vary in quality from theater to theater -- at least that's the way it was in 2012. I know that Fathom was essentially bought by AMC, Cinemark and Regal right at the end of last year, so it has changed ownership. Maybe that means all showings now use the 2K or 4K cinema projectors.
My Season Two screening was plagued with technical issues (sound problems and delayed by over an hour) and looked very, very murky and dark. And this was at the AMC Burbank 16. It was relegated to one of their smaller screens. It was so underwhelming, I refused to see "The Best of Both Worlds" the following year. Which is a shame, as I probably looked forward to that the most.