Avoid stereotypes. Over-generalizing is one of the most common ways writers ruin a character. This isn't to say that observed cultural tendencies aren't valid. For example, creating a Mexican-American character with a passion for Mexican history and a commitment to Mexican culture isn't a bad idea, but the way to avoid creating caricatures of Hispanic characters is to give them their own personal attributes independent of their cultural roots to show that every person is inherently unique.
Don't confuse starkly different Hispanic heritage groups. One main problem is writers ignorant of history creating Mexicans who talk or act like Spaniards and vice versa. Details like the term "castillian" used by Spaniards to define central Spanish culture are to be used correctly. Paying attention to linguistic and cultural aspects of the 'old world' in Spain will help you avoid this problem as a writer.
Know histories of Hispanic countries. While separating your character's cultural identity, whether Spanish or Latin American, it helps to recognize the way that Spaniards made their way into Latin America in the first place. Even if the complex history of Latin America is not alluded to directly in your work, acknowledging it will make your characters more authentic.
Observe Hispanic communities in the region you will be writing about. Basing characters on direct observations and experiences is one way to keep them real. Your characters don't need to be carbon copies of real individuals: a good fiction writer creates an abstract and develops characters from it to give them both originality and authenticity.
Don't let audience attraction ruin your characters. Avoid trying to tell readers what they want to hear, or basing characterizations on anything but your own creative ideas and experiences. The temptation to cater to a readership is a common problem with writing, and character development in particular. Be sure that you are developing a character according to their role in your work, and not according to some outside criteria to please readers.