Costa Ricans are generally very affectionate and physically expressive of their affections. It isn't unusual to see couples holding hands, walking with linked arms or hugging and kissing. You should feel free to express your affection, yet avoid any explicitly sexual public behavior (e.g., dancing close is common, but grinding is frowned upon).
While you may be used to wearing shorts in hot weather no matter where you are, in Costa Rica it's common for people to dress more conservatively when out in the city. Therefore, while it may be hot, avoid wearing shorts in city areas. Shorts are, however, acceptable at the beach or in more rural areas.
In America, for example, there are fewer rules governing certain areas of social behavior than in Costa Rica. For instance, if invited to someone's home for dinner, you would be considered rude not to bring a gift of flowers, chocolates or wine. Never rest your feet on anything but a footstool. Costa Ricans also place a high value on dignity, and doing anything that could be seen as embarrassing another person in public is frowned upon, even if meant as a friendly joke.