Doc, since you say people are renting by the week, are owners subject to collecting lodging and every other tax that gets passed on to the poor tourist (no wonder people stay with relatives)? In many places, less than a 30-day rental agreement makes you in essence, a hotel--subject to all the other taxes that normal landlords aren't. If the current owner is renting on the QT by the week and not reporting it as a hotel, you can just about bet that you probably won't be able to get away with the same thing--someone there all the time will probably complain about it. So, that is another reason to read the Association rules before you buy.
Make sure you get a copy of the owner's tax returns on the property--anyone can say "well, you can make so-and-so", but check into what they reported, and what they took as expenses. And, if the agent is telling you what rents go for, find out if that is before or after management company expenses--if you're renting by the week, management company expenses can really cut into your profits. We have looked into the beach rentals (cabins) in different areas--both from the staying at and from the owning/renting aspect. The agencies that do the managing want like 40% of collected rents! Now, part of that includes housekeeping and such, but remember, if it is a weekly rental, you also won't be able to get tenants to pay for their own utilities, which can eat into profits no matter how much you do to make the place energy efficient. And you can only charge what the market will bear rent-wise.