Yes, old Gretsch guitars have issues with both neck set and with binding falling off.
The thing is, as ALL of these set-neck archtop or acoustic guitars keep getting older, neck re-sets will be inevitable-- it just happens to Gretsches first. I've got a Gibson in the shop having a neck re-set this year, had one of my Epiphones done last year, and another of my Epiphones done a few years before that. Any Martin old enough to have Brazilian rosewood back and sides (pre-1969) almost assuredly needs a neck set if it hasn't had one already. Time marches forward and takes its toll... but at this point, many of the sought-after Gretsches have already been done, and the "better" guitars are just now getting to the point where they're folding in half...
Obviously a real vintage example will maintain its value and (when properly maintained) if it's a 'good one,' will very likely have 'something special' that none of the modern re-creations have. but a vintage (1950s single cutaway) 6120 will be pricey indeed, out of reach of most players. The big difficulty with vintage Gretsch is that they tended to re-design their guitars (sometimes radically) each year or every few years, sort of like car manufacturers. Even changing body styles (the 6120 went to a double cutaway at some point), adding features, etc. So the "desirable" variants tend to have only been made for a few years max, and the less-desirable variants often have little to do with the desirable ones other than the model name/number (which can get confusing).
Gretsch guitars are currently under the umbrella of FMIC (Fender) and have a similar approach to tiered cost and quality. At the top are the custom shop or "master built" guitars, which tend to be VERY nice instruments built up to the level of (or in Gretsch's case, very likely BEYOND) the level of objective build quality in the 1950s and 1960s. You buy one of these guitars, you get to learn the name of the luthier who built it (true for Fender, I think so for Gretsch as well, but not positive). Not dirt-cheap, but very often less money than a vintage example (especially for something really desirable like a 6120).
On the far other end of the scale, the "Electromatic" line are, I believe, made in Korea and are about what you'd expect-- built with mechanized precision, but to a lower price point (reflected in finish material and parts quality most of all; fit and finish tends to be pretty OK considering the cost).
With a 6120 the big decision (to me) is if you want a mid-'50s style (with DeArmond "Dynasonic" pickups) or a late '50s-style (with Gretsch "FilterTron" pickups).
Pickups of both styles are the biggest challenge for modern Gretsch-type guitars. Unlike Gibson and Fender style pickups, your options for aftermarket/upgrade are limited. TV Jones makes them (and has for years) in both styles. Jason Lollar and Curtis Novak each make a FilterTron copy. The Dynasonic is a very mechanically complex design with lots of specialized parts (and I'd assume tooling) so fewer aftermarket winders are willing to tool up and take it on.
Stepping outside of 6120 world, Gretsch also made a coupe of other pickups, the single-coil budget-minded "Hi-LoTron" (less sought after by vintage aficionados), the blade-magnet SuperTron, and some others. But the Dynasonic and FilterTron are synonymous with "Gretsch" to most, so I'd look for a guitar with one of those.