I've used it 4 times so far. Great experiences with 2, horrible with 1, and we are heading toward rental #4 in Tulum next week (currently in a VRBO rental in Oaxaca till then).
Overall, I love it. We can get 2-3 BR apartments with full kitchen and decent amenities for the price of a low to mid grade hotel room. Spending a week in a hotel room isn't that much fun, and much less so with 3 kids. Spending a week or two in a decent to nice apartment or house for a week or two is very nice and relaxing. We cook some meals, have separate areas to relax, and different rooms for sleeping.
The only bad experience was a really dirty (but very cheap) place in Quebec City, Canada. Reviews were generally very positive, but we realized the landlord rented just a bedroom sometimes and other times rented the whole apartment. The bedroom was clean enough as was the bathroom. The common areas like living room and kitchen were pretty gross (cat hair, cat poop, cat litter, more cat hair, grime all over the floors, greasy dirty rugs, etc). We cancelled the rental as soon as we could. After contacting Airbnb, they suggested we should have called them immediately and they would have found us a different place and provided a discount to help if the prices were higher. Instead, they offered a full refund of all nights plus their fee and gave us an extra $150 to use toward a future rental (just used it in Mexico City). Very happy customer here even though the one rental didn't work out.
Just read the reviews and ask questions if you are concerned. I also wouldn't go for the absolute cheapest properties unless you don't mind dirt or feel like taking a risk. Also look at all the filters in the search engine. I would screen out apartments that allow smoking and allow pets since I'm paranoid about getting a stinky dirty place now.