We heard all these stories before we booked, but had no problems. It certainly wouldn't stop me hiring an apartment again. It's the only way to have an authentic New York experience and also very affordable.
It may be perhaps more affordable but there are many scams also associated with the likes of holiday rental websites. The whole enterprise is not without a degree of risk for both the renter and the resident particularly in NYC where this practice has been outlawed.
People have been fined for renting out their apartment for visitors when they have not been there at the same time. The fines for the resident are steep as well and people can be evicted.
SF and New Orleans to name two other cities have equally strict laws on short term lets to visitors. Its not worth the risk.
Aside from local laws, many large apartment buildngs in NYC are condominiums or co-operatives (co-ops), and they are governed by rules about what their residents can and can not do. Most likely, their rules prohibit renting apartments to tourists on a weekly or daily basis. If the neighbours are fed up with a resident who has tourists coming in and out on a weekly basis, and if they don't want strangers to have copies of keys to the building, they will check with the janitor or management company to find out what's going on.
I second the choice of the Harlem Flophouse: its supercheap, really lovely (have a look at some of the photos here: www.harlemflophouse.com/), and the A/D trains run straight from 125th Street to 59th, which means that you can get to mid-town within minutes. The bathrooms are shared, but they're sinks in each of the rooms, and I've never had to wait to use the bathroom (I usually visit New York twice a year, and stay there for a week or two each time). However, the last time, there was building work across the Street starting from around 8 am during the weekdays, and running until about 3 pm, so not so good for a lie-in (though you don't hear the noise at all if you've got a room at the back of the house). Also, there are no TVs, aircon or a front desk: it feels more like staying at an eccentric, rich aunt's house, rather than a hotel, which might be a good or a bad thing, depending on your point of view!
Interested if anyone else who has actually used airbnb felt it was such a big 'risk'. We had fully read up on a these issues but for us it was such s fantastic experience. Some people wouldn't take the 'risk' of booking outside a travel agents. Airbnb hold your money until you have inspected the apartment and all is as expected in arrival. I wouldn't go on and on about it unless I really felt it was a perfectly safe and acceptable option for someone in a budget.