Someone may have said this, stopped reading shortly when some complained about games that have worked fine for me... but, I believe in MOST cases, the problems we see won't be on a global scale. I.E. the % of games that we have a problem with might be just fine for 90% of the user base. We can get into some really funny math here, especially since we don't have solid numbers.
For my part, I have only seen a few. One game is missing most of the art on the screen, but it wasn't rated for the OS I tried to run it on so I can't count it. Theoretically, it should work... but as the description indicates... it doesn't.
I believe the Thief games did not work for me (windows 7) without tweaking, but I need to format and try again as I may have had some remnants of the CD versions. Also, Thief 1 does not work on Windows 8 for me at all (fresh install).
The Book of Unwritten Tales required me to turn off dual video cards at the hardware level (a profile was not sufficient).
Broken Sword 4 has a location where you can get stuck in the game. (physically stuck). It took me about 30 minutes of in game button mashing to finally break free (multiple reloads and a quick forum search indicates this problem was prominent... also, a cutscene put you in this stuck position, so it wasn't an issue where people wandered where they shouldn't) I won't argue who was responsible for fixing the bug, but it wasn't fixed in the GOG version.
I agree with you OP, when I install a GOG game, I just expect it to work. I have re-purchased many games that I already own for the advertised reason of a no-fuss and compatible install. So far, I have not been extremely disappointed, but they do have some work to do on some existing titles.