Should the cover design have different versions for brick-and-mortar stores and for digital presentation?[/quote
Yes, of course. You cannot have the same cover, it simply doesn't work. For one, again, you're looking a much smaller thing to read on - Iphone for example. So, if you look at a, say, 3.5 PHB, or, even worse, a 4e PHB, that's not going to work in a titchy little image. Different mediums require different presentations.
Should the use of art change depending upon the sales channel?
Abso-freaking-lutely. Tables don't work on a smaller e-reader like a smart phone. They just don't. I don't want big honking pictures in my ebook - I don't want any pictures at all. They serve little to no purpose and make reading very difficult. Also, the layout of the book MUST be different. Three columns DON'T WORK on e-readers.
Does a change of cover treatment cause confusion with the buyers?
Possibly, but, we're talking about different venues here. If I'm looking for, say, a Monster Manual, I'm probably not going to buy the books cold. I'm already going to know what a Monster Manual is. And, if the e-retailer site is up to snuff, it should explain exactly what I'm buying anyway. I mean, look at novels. How many covers are there for, say, Harry Potter novels? I know of at least half a dozen for each novel - all targetted at different audiences. And the e-versions are also different as well.
Do they notice or care about the differences in a cover from one version of the book to the next?
I'm not sure what this means honestly? You mean, like Monster Manual 1 or 2, or do you mean an electronic vs print version?
Does the role of the cover have a different purpose to the consumer in the different mediums, or it simply a business issue?
Again, absolutely. A print book's cover is there to attract your eye. You're looking at that wall of books, and a cool cover brings people over to look at it. Plus, having a last name begin with H or thereabouts usually puts your book at eye level in most book stores.

But, an Ebook buyer probably already has some idea about what he or she is looking for. Sure, people "browse" e-retailers, but, I think it's much more likely that you get people who are hitting certain author's or related works. That sort of thing.
Should a digital cover try to look like a book cover on the virtual bookshelf, or is that an antiquated concept?
I have tried pretty much every e-reader program for the Iphone/Ipad. The I-reader app blows chunks. The absolute best one is Stanza. Which doesn't have a "virtual bookshelf" per se. It shows the little cover images down the left with the book titles in big letters in the right. Works great. My opinion would be no, but, then again, Kindle and Apple would disagree with me, so, hey, they probably know better than me.