Assuming everyone speaks English
Even if you're not so big on stuff like "history," you should know that the Caribbean was colonized by the Spanish, French, English, Dutch, and a few other countries over the better part of the past millennium. Accordingly, people do not speak the same language in every country, and the dialects of the languages they speak are completely different.
Take the British West Indies, where English is the dominant language. The accents and dialects locals use can be impossible to understand (Shottas, a Jamaican cult-classic film, requires subtitles). The Spanish you'll hear in Cuba can be incomprehensible to Dominicans and Puerto Ricans. Dutch is handy in the Leeward Antilles, but the common language of Aruba is Papiamento. And you'll hear varying versions of French patois in Haiti, St. Lucia, Dominica, Martinique, and other former French territories. Lucky for you, many Caribbean people speak three or four languages. But don't assume they will speak English (or, inversely, that someone doesn't understand what you're saying perfectly well).