We love nopales. We DON'T love prickly pear thorns which is why we don't buy fresh pads here. I had read some time ago about thornless varieties. Given that <ahem> some garden catalogs and websites can be a little heavy in their claims of a plant's good points, and gloss over the bad, can anyone comment on thornless prickly pear?

I have some that are nearly thornless and much better than most, but I don't think I've ever seen one that is completely thornless.

Sorry to be a stickler, but they are not thorns, they are spines.

There are pretty much spineless varieties of Opuntia ficus-indica that were selected and propagated for their lack of spines - does not mean you do not get the occasional pad with some spines, like plantmanager says. However the main issue with eating prickly pear pads is the glochids rather than the spines, even most spineless Opuntias tend to still have glochids and those little hairs are way worse than just about any spines.
You would buy/harvest young O. ficus indica pads (or young pads from other known edible prickly pears) and then with a filleting knife just slice off all glochids/spines and then you can prepare them.
I have had them several different ways, the main thing to do is avoid getting them slimy which happens easily. I have had them pickled (and in salsas), (deep) fried, and grilled and in all those ways they have been good. I have had them in some soups in which they have been good, but those cooking methods all avoid getting them slimy, once they come out slimy they are not very good in my opinion... I have made them myself on the grill and that came out well - when grilling them quickly on high heat, low heat and slow tend to get them slimy.

Opuntia cacanapa 'Ellisiana' is spineless and glochid-free for the most part. Gets big too and takes cold and heat.

The preparation of nopales here for cooking (as I would assume is typical through most of Mexico) always involves the removal of the areoles from the pad. Which an expert can do with a sharp knife in about 5 seconds.

You want to look for young pads when you have the choice, because they are the tastiest, and they are also less spiny at that point to start with. I know this because I can do my prickly pear pruning without gloves if I get in there very early in the season. To some extent the youngness of the pad overrides whatever concerns about spines that you might have based on a full grown adult. Our "spineless" nopales are not exactly that but it doesn't matter too much in the end.

Typically the plants in nature (as opposed to varieties selected for cultivation) are really well armed for self-protection, and you wouldn't generally want to mess with those in the first place.