Always be alert and aware of your surroundings.
 

Never leave valuables in plain site in your car or beach or wherever they are unguarded in plain view, even for a moment. Do not flash a lot of money or wear valuable jewelry. 

At all times be on the lookout for pickpockets or crowds of young people who may wish to relieve you of your possessions. Snatch and run is a technique used by some, so again, be aware.  

It is generally acceptable to just carry with you a copy of the main page and page showing entry date of your passport.

Compared to what you make, you seem rich to many Ticos. Also, things you have that are not that expensive may still seem valuable and worth stealing to someone else. This includes towels, flip flops, and sunglasses. You can probably afford to replace these, but it still seems puzzling and is inconvenient and still a shock.

In an emergency, call 911, but they may not speak English.