I've edited a variety of works for different people over the years. From high school through college into today, when it went from friends and friends of friends asking me to edit term papers and fiction, into today when I've spent my professional life editing newspaper articles and press releases, I've held onto one single practice that has always served me well.
Now, some people might say reading aloud is a crutch, that we shouldn't rely on it as a be-all, end-all editing tool to craft proper sentences. I agree with them for the most part; there's no real substitute for knowing the rules of grammar -- what a compound modifier is and how to use it, the proper method of comma placement, how to craft a sentence so your meaning is clearly understood, etc. All these things can be accomplished without reading a single line aloud.
However, and other people have said something similar, I can hear grammar mistakes quicker when a sentence is read aloud than when it's read silently. Good writing means nothing if you trip over the words; any speechwriter worth their salt will tell you that. Good fiction is the same way. If the rhythms of the words are off as we read them, then the story suffers. A technically correct sentence may be an example of good writing in the academic world, but if the cadence of the words doesn't flow naturally when someone reads it aloud then that sentence wouldn't work in a novel.
Since I love me some examples, I'd like you to read the following two sentences aloud:
John went down to the corner store.
John done gone down to the corner store.
Now, the second one is clearly incorrect grammar. If you were reading merely for proper grammar, you'd change "John done gone down" quicker than anything. However, if you read both sentences aloud, you'll see that they both communicate the main idea in a clear cadence. The second sentence is merely written in a dialect, while the first sentence is not.
Someone reading the second sentence without reading it aloud would probably change the sentence. I know I would, unless the context the sentence occurred it merited leaving it in dialect like that. Reading aloud has the added benefit of allowing you to see if the proper emotions are evoked within a certain section. However, and this is the key part, do not put any inflection on the words. If you have to add inflection to a sentence in order to make it evoke sadness, or anger, or anything like that, then you've written the section wrong. The words need to speak for themselves in all cases. Because let's face it: most people who are reading your book/short story/whatever aren't going to be listening to it as an audiobook.
Do you read your work aloud, dear readers? How has it helped you?