One of the most frequent, especially by people who have never studied Italian, is the pronunciation of diphthongs as if they were distinct vowels. Diphthongs are vowel combinations pronounced together. If you know nothing about diphthongs (is that an ugly word or what?), you can find out more at the Wikipedia entry here. The article is terrifyingly long and detailed, and even includes examples from Faroese. That might come in handy.
Now, I wanted to do this post because these mistakes really annoy me. Let's look at some common instances. Pinot Grigio. The wine. Lots and lots of people say: Pinot "GREE-jee-oh." If you are one of these people, I want you to stop. The final -io is a diphthong, and should be pronounced together. Like GREE-joh. How about the common name Giuseppe? Have you been going around saying "GEE-ooh-zeppeh"? Don't. It's "JOO-zeppeh." Same goes for Giovanni- "joe-VAHN-nee."
Not all vowel combinations are diphthongs. One of the first words you learn in Italian is the pronoun io, I. The two vowels are distinct (eeh-oh), unlike the equivalent Spanish yo. Same goes for the words zio (uncle) and zia (aunt). But most vowel combinations in Italian will in fact be diphthongs. Let that be your default.
There are also triphthongs such as buoi, oxen, pronounced bwoy and not boo-oh-ee. But these are unusual and I wouldn't worry about them too much.
