Chuck, I would say that the specs that really matter the most, used or new, are the runout of the spindle and the flatness of the bed/ways -- in that order. If the new machine specifies .005 backlash and you measure .007, I wouldn't bother with a warranty claim, not unless you find something else wrong.
If you haven't read the mermac articles that someone linked to above, I highly recommend them. These were very helpful for me when I got started. Note in particular that if you buy a used lathe, you will very likely have some bed wear ... but it might still be perfectly usable. My old Cinci Traytop has some wear, but I've been able to turn out parts to the limit of accuracy that I can measure.
That last statement is really important -- as a home user, I don't have the special temperature controlled room and ultra-sensitive tools to measure to .00001, nor do I have the slightest need. I am not convinced that I am yet able to get a
repeatable measurement within .0001 with my best micrometer -- my "touch" is just not that good yet. But I can get within .0005 if I need to. Measuring within .001 is easy, and hardly ever do I really need anything closer than .001. Actually, much of the time .005 is all I really need (though I still shoot for .001 for pride
).
Note that I'm talking about "absolute" measurements here. As a home/hobby user, the only time I need to be within really close tolerances is when I am fitting parts together -- which I will fine-tune for the perfect fit. If I need to get a super-close sliding fit between two parts, for example, I may not be sure -- or care -- that one part is .5000 instead of .5005, or even .505, but I am sure that I have a sufficiently close fit
between the parts -- certainly within .0005, and maybe even better than that.