I've seen much worse but don't remember what ones.
This is a bit of an example:
http://www.onsemi.com/pub/Collateral/LP2950-D.PDFFig.17, note instability for low ESR at 0.1uF load. (This isn't a good example, because they claim stability for more C, at any reasonable ESR. 0.1uF is pretty small, easily met by the bypasses on a couple of loads!)
Note also, while they don't give GND/ADJ pin current, they do at least give Fig.6, which is on the scale of 100s uA, and you do see a blip where it's struggling, but it's only struggling to the tune of say 20-50uA, not crazy.
So I wouldn't mind this one. It has risk factors (bipolar, C and ESR limits). On closer inspection, they are hardly insurmountable. The documentation seems adequate to support this conclusion.
If you see one that merely claims (and this may be in the headline text, or buried deep in the application section) that it needs C and ESR of such-and-such range, treat it suspiciously. If you see no documentation whatsoever about the matter, run away!
Peeking in my junkbox, I see
https://www.alldatasheet.com/datasheet-pdf/pdf/53200/FAIRCHILD/KA378R12C.html which doesn't make any claims about capacitance (except to suggest >47uF being somehow helpful), and which shows dropout current consumption in dramatic fashion!
Tim