Are screwed on pot handles an indication of quality?
Briefly, no.  Screwed on handles usually are found on cheaper cookware, but it doesn't necessarily mean the pan overall is of poor quality.

There used to be a contention that riveted handles were the strongest and an indicator of quality cookware.  Also, welding and various screw attachments (which frequently also contained welds) used to fail more frequently.

But in cookware that's manufactured now, it's really a design choice.  Some people like the traditional look of rivets, while others find them annoying to clean.  And many cheap manufacturers now use cheap steels for rivets, meaning in some cases they're just as likely (if not more likely) to fail as other constructions.

Screwed on handles are generally used on cheaper, lower-quality pans, but not exclusively.  They can take a number of different forms, sometimes screwing onto a base that is welded to the pan (and thus creating more points of failure), sometimes screwed onto a base that sticks out but is manufactured from a single piece of metal with the pan, and occasionally screwing directly into the side of a pan.  The biggest problem with screwed on handles is that they're generally more vulnerable to coming loose.  On the other hand, when they do come loose, they can often be more easily tightened and thus repaired than welds or rivets (which would generally need to be sent out for a specialist repair).  Also, on cheaper pans, the handle materials tend to be cheaper too and may crack and warp over time, so a screw attachment can make it much easier to simply buy and install a replacement handle yourself.

The key is just being conscious of screwed on handles and tightening them if they ever start to wobble even a bit.  (You do not want a pan or pot handle to ever come off unexpectedly while moving boiling hot food around.)

Unless you're talking about unusual pans (particularly very heavy pans, like thick copper) or unless you tend to fling your pans around with a lot of force (like if you love to do the "saute toss" repeatedly every day with a fully-loaded skillet), most methods for attaching handles can function fine.