Is "warm" a compliment or a criticism?

'Warm' is inherently neither good nor bad. It descrobes a tonal balance that has more energy in the lower half--say, below 500Hz--than in the upper half. (A tonal balance having more high-frequency energy is called 'bright'.)

Warmth is absolutely a coloration, an error, but usually it sounds wonderful if not overdone. But warm becomes 'thick' rather soon.

So whether 'warm' is good or bad is truly a matter of opinion, but WHAT it is is rather commonly accepted.
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Gunbei is right.

Curves=good. Skinny straight stick chick= need sandwich.

For audio equipment, I've frequently heard tubes described as yielding a "warm" or "full" sound. When I listen to my Cary SLI-80 Signature driving my Revels however, I don't notice "warm" so much as "rounded yet detailed".

I think the term "warm" can be interpreted as good or bad- as you stated. So for audio, it's probably a fairly ambiguous and poor term.

At the least, "warm" means that the sound is not shrill or harsh. Most anyone would consider that great news. But beyond that, the meaning seems to depend on writer / speaker and the situation. A system that portrays the beauty of midrange, such as female singer or sax, can be described as warm. But "overly warm" suggests that details are being sacrificed in exchange for presentation of a sound that is pleasant, but lacking in realism.

For many years, it seemed that most transistor gear had a harshness or graininess to it, and so "warm" was a welcome relief from this problem. Todays best systems seem to sound realistic without being either grainy or overly rich or colored ("warm"), and hence this term can had positive or negative connotations.

While Jeffreybehr makes a valid point regarding a possible hump in the FR between 100-300Hz (that could be even "lumpy" for some people) or alternatively a notch in the 2-6kHz region, IME the term "warm" is usually used in a positive vein:
the sound is full "enough" -- i.e. there's sufficient energy but not more than necessary -- in that region.

Mind you, one person's "warm" could be the next person's "lumpy" ESPECIALLY relative to the spl at which this comment is being made: at low spl our ears are less sensitive at 100Hz than they are at 3kHz!

One man's ceiling is another man's floor-Paul Simon