What seperates "hi-fi" from "mid-fi" in cdp's?

Gthrush is right, in my view, but if you're looking for a philosophical analysis, my feeling is that better power supplies and analog stages, rather than bits and digital chips, are what separate the pedestrian CDPs from the best.

Straight listening helps, IMHO, only if one has an experience in that - one should know what to listen to, and what nuances to pay attention on...
I don't think there are characteristics that would clearly distinguish mid-fi from hi-fi... Too many manufacturers claim such things as "oversized power supply", but only some of them really benefit form it from sound quality perspective. Price doesn't mean anything eiher. I think the only way to evaluate a component is a combination of gathering info about unit's design advantages along with looking for opinions, and with listening.

You may want to limit your selection to those models with
a 24/96 or 24/192 DAC. Players with a 16/44.1 are outdated,
there are several models with the 24 bits DAC to fit every
budget. 24 bit DAC will give you the best sound with regular compact disks. Hope this hepls.

I strongly w/Hepl. Slightly obsolete digital gear sells at a dramatic discount. I would think if you were looking for entry level prices for a CDP, you would go with an older model from a high end manufacturer, like CAL, Wadia, Meridien, EMC, Mephisto, even Sony (for example, DVP7000ES for $2-300.00, which also plays DVDs)

It's the same thing that seperates every other component from great to not-so-great: the power supply and output stages. The better cdp's are usually more expensive because they use premium parts for power supply, filter caps, voltage and current regulation stages, isolation of power supply for signal and operational (LED's, mechanical, controls, etc), shielding, output devices, and overall circuitry design of the output stages.

You can't really go by the type of DAC or drive mechanism alone to judge whether or not you're getting a quality product. Most low end cdp's that vary in price will use the dame DAC for example, but the price difference is based on convenience features. The difference in sound, for example, of the Marantz 63 and the 63SE is night and day - all due to the power supply upgrade in the 63SE.