Sure, that can happen. (Idunno, what more were you expecting to hear?

)
If the standoff heights are uneven, the board warps... if the centers are uneven, the screws gouge into the holes, and may warp the PCB in odd ways (stretching / squashing around the sidewall contact, warping). Star and split washers bite into the board and scrape away material. No washers at all and the board itself cold-flows under the screw, coming loose.
Some of the best methods are precisely located holes with precision fasteners, such as snap-ins (e.g.,
PEM Snap-Tops), or something more compliant (and lower tolerance), such as plastic snaps (most are quite flexible, but by the same token, won't retain your board very rigidly, if that matters -- e.g., putting too much strain on a board-to-board connector, during shock and vibration), or using good old fashioned standoffs, screws going through holes large enough (to accommodate the screw tolerance itself, plus manufacturing tolerance, plus assembly tolerance -- e.g., a 5/32" clearance hole for #6 threads is common), with good spring washers (wave or cone type) that will maintain spring force as the board material moves underneath, without damaging the board in the process -- especially important if you'll be removing the board often.
To handle all of that, you need enough clearance to account for the washer (usually even bigger than the screw head), plus assembly tolerances (the washer is loose around the screw, and the screw is loose inside the board), and a little slop for good measure (20 mil?). I guess you're already outside of that, so... you'll want to be careful to add instruction that they be assembled gingerly. Even then, you'll probably expect some assembly related fallout. So you'll need to employ an inspection, quality assurance and process improvement program... PITA.
As long as your standoffs are good and parallel, you won't have to worry about board flex. You could calculate how much. I don't know how much it takes before it's a problem, but on the plus side, it should be achievable to manufacture such a thing, like, without having to lap the surfaces optically parallel or something horrible like that.
In that regard, you'll probably have the best results with a milled enclosure (all mating surfaces within the specified tolerances; for CNC machining, usually a few thou is easy enough to do quickly*), second probably loose standoffs on a flat, stiff plate, a close third probably machine-pressed inserts (like the PEM nuts and standoffs and studs for sheetmetal), then hand assembly last (you can press those inserts by hand with an arbor press just fine, but if you're not doing it carefully..).
*Of course, we're talking design of an enclosure, milling it, and covering the cost of materials and machine time. "Quick" being relative to that...
Tim