I think some of this is inherent to the model, and part of the problem is that businesses aren't building the right expectation in to their budget. They're thinking in terms of getting a bunch of ordinary customers in by giving them 50% off of an entree, and given their metrics on ordinary customers, that seems like a good deal -- a coupon of the same sort, sent out in one of those mailers, would pay for itself easily. But Groupon is bringing in a different set of customers --
low-value customers who don't provide much repeat business and often pick a fight over trying to get an even steeper discount.
Wait staff often complain of Groupon'ers either not tipping at all, or tipping a low percentage and basing their low percentage off of the discounted bill (such that the net tip is like 1/4 to 1/3 of what it would normally be for the same meal.) Some places complain about Groupon'ers overstaying their welcome -- they come in for half price entrees, don't order appetizers or drinks or dessert, and stay at the table for 3 hours eating wave after wave of complimentary breadsticks. They're the ones still at the water park when the staff locked the gates ten minutes ago. They come in multiple times in the next week trying to return something for full price or otherwise scam the store. Many places report an excess of complaints of the "I'd like to speak to your manager, you're doing a terrible job" variety directed at their best employees, because people are unhappy paying 50% when they think they can somehow get it down to 45%, or they're unhappy paying 50% for 100% of the experience when they think they can stretch it to 105% of the experience.
This doesn't happen to every company, but it does happen to some companies and leaves them feeling pretty burned.