I'm pregnant and traveling to Costa Rica.

I doubt it. Just make sure you are fully insured and the baby is fully insured too. Most airlines heap lots of trouble for late pregnancies (seventh or eighth months is the limit I think). Maybe you should also have a notarized certificate signed by your doctor that you're expecting a child at  around this date etc.

Enjoy Costa Rica, and enjoy the baby :-) 

I think there are some precautions needed to be taken when flying with a baby:

• choose an aisle seat so you can walk around.
  
• The air on the plane is very low on humidity you are going to need some saltwater nasal drops to relive his airways.
• ears pain as well because of the pressure , let the baby suck a lot.