Dialogue obviously should be read aloud, preferably with you doing the different voices to check that you're getting different rhythms of speech for each character. A common mistake is for all the characters in a story to speak with a single voice pattern, presumably that of the author. But you should read it all, dialogue and prose alike, with a pen in your hand. Does it read smoothly? Does it flow? Does it make sense?
It's the easiest way of checking for grammatical errors and repetitions because often what looks okay on the page, doesn't work when it's spoken. At the very least, reading aloud shows us where the punctuation should go. Listen, and you can also detect the rise of one's voice where there should be commas, and the fall when there's a full stop. If you don't believe me, try playing The Shopping Game with a friend.
For those who don't know it, you start "I went shopping and I bought - " and then you name something, for example, a chair. The next person begins, "I went shopping and I bought a chair and - and they name something, for example, a mouse. Then onto the next person. "I went shopping and I bought a chair, a mouse and a cat. " "I went shopping and I bought a chair, a mouse, a cat and a pencil, "and so on. The natural thing is to let the voice rise after each item on the list until the very last one when the voice falls. In other words, comma, comma, comma, full stop.
Perhaps because I used to be an actor, reading my work aloud has always seemed a natural part of writing, both as I go along and as I edit. I sit at my desk doing the voices and the fact my family often ask things like who I was on the phone to doesn't bother me at all. It's a habit, and a good one to get into.