We purchased on GC a couple of years ago. As Doctorfish mentioned, it is very straightforward - essentially the same process as purchasing in the States, except that titles are registered by the government so you do not need title insurance. We purchased a condo rather than a stand alone residence primarily because the financials worked out much better, and secondarily because we wanted someone watching the property while we were away (we spend only 3-4 months there each year). Our condo has a great management team that also serves as a rental agency, and we put our unit up for rental when we are not there. The management team is available to the guests, just like a hotel, and provides daily cleaning service and maintenance, so when we return the place looks better than when we left.
Before purchasing I did extensive financial analysis of about 15 properties to see what our net costs would be to own, plus factoring the relative desirability of each property. The costs of insurance, maintenance, utilities, etc are typically lower for a condo than a stand-alone property, as you are spreading the costs over a wider number of properties. But each property varies in the total monthly costs, and the costs per square foot (which was a key metric for us). In addition to the monthly out of pocket costs are the commission or other fees that go to the management group who handle rentals, plus the opportunity cost of tying up finds in the property instead of investing them in something else.
On the revenue side are the rental fees you will collect and the estimated number of days you will be able to rent the property. Additional there is the potential appreciation - although we decided not to include this in our analysis as you can't count on it (although we've seen some nice appreciation over the past couple of years).
We originally came looking for the least expensive place we could find north of SMB. The most interesting thing that came out of my analysis, however, was that the more you pay, the more the place will pay for itself. Your out of pocket costs go up with a larger, more expensive property, of course. But rental revenue goes up faster that costs (at least for the 15 properties I looked at). It is more difficult to rent a less desirable property and the daily rent is lower, so in net the he least expensive place we looked at would never have covered our out of pocket costs. On the other hand, the place we ended up purchasing cost about 4 times as much, but even though we use it during the entire high season, the rent from the off season has covered 100% of our out of pocket costs (condo fee, insurance, utilities, cleaning, maintenance, etc.), so far. And as long as the property appreciates as much as it has, we essentially have had a free place.
The final test was the worst-case scenario assuming we had zero rent and zero appreciation (which has pretty much a zero probability of happening). In that case the net cost to us for the property we bought would be exactly the same cost as if we had come down as renters and just rented the place at the going rate. Now, we would not have rented as nice a place, but at least we would be getting our money's worth.
Finally, other than the stamp tax the buyer pays on the property (less the value of any "chattel" - furniture and fixtures) there is no income or capital gains tax. If you buy property worth more than $500,000 (I believe) than getting residency is pretty straightforward but expensive. We got Cayman drivers licences, and that seems to get us most of the benefits of residency (various discounts here and there).
We did debate the issue of being "stuck" in one place vs traveling around to other places, but the benefit of having all our clothes, diving equipment, etc. stored at our place and being able to jump on a plane with just a backpack was more than worth it. Plus we have gotten to know lot of people to hang or dive with. I'm a musician and have met a bunch of other musicians and have been able to sit in with a few bands down there. We don't have to spend time learning the ins an outs of the place. It really is a peaceful and stress free vacation for us (well, except for all the crazy hoops we go through to import our dog each year - but I even know the folks at the Cayman Ag Dept now so that's another benefit of returning to the same place each year).
Anyway - good luck to anyone who decides to buy in the Cayman's!