Tourism is potentially one of PR's comparative advantages. Agriculture is another. There may be more, but those two strike me as the best things PR has going in terms of her economy.
I think the challenges in developing the PR tourism sector are largely cultural. There simply isn't a commitment to customer service in PR. This isn't to say that you can't find employees who will "hustle", but as a general rule, that's not part of the culture.
The second challenge is language. Last time I checked, the overwhelming majority of tourists to PR come from the mainland (roughly 95% if memory serves). English, like it or not, is the language of business, yet many Puerto Ricans refuse to speak it, if they learn it at all. Don't get me wrong, I'm not suggesting that they abandon Spanish, or that expats shouldn't learn Spanish. But if you want to succeed in what is by definition an international business, you better learn the languages that your customers will speak.
Apart from these two problems, I think PR suffers from a different "PR" problem -- that is public relations. Most folks on the mainland don't think of Puerto Rico when they think of an exotic Caribbean vacation. And when they do think of Puerto Rico, they think of crime and poverty.
Oh, to tekrider's point, I agree that "economic" issues play a role. PR must abide by federal minimum wage, inflating costs relative to the other islands.