This probably can be said of just about anywhere, but beware of unauthorized "guides" who approach you inside the park. They may strike up a conversation and start telling you about the sites-- seeming very friendly and knowledgable-- only to demand an extortionate amount of money in return. The tourist police don't seem to mind.
It's worth it to get an authorized guide on your way in, since there is so much to learn about this fascinating place!
As you walk around the city you will be occasionally approached by people trying to sell ancient coins, and other items supposedly dug from the ruins. The guys aren't pushy, and the items they sell are quite possibly genuine, given the ease at which some people have reported making their own discoveries. The problem is that it is illegal, not to mention immoral, to export antiquities from the country without a licence. So don't bother.
There are plenty of well armed security guards wandering the ruins, and they are there for your protection. It's not that anything is likely to kick off, but the Jordanians want to convince tourists of how much they are dedicated to their protection.