For a speechwriter, few things are more painful than hearing your principal stumble over the text - especially if it is your fault. There is no way to prevent this completely, but reading the text aloud before you hand it in cuts down on the chances of embarrassing moments and eliminates the pangs of guilt (mostly).
Yet, a significant percent of the speechwriters I have known and worked with count on listening to the voices in their heads, and they hand in copy that suffers before the audience, time and time again. I can tell immediately if a speech (that may have looked good on paper) has never been read aloud. And this is such an obsession for me, that I have actually confirmed read/never read with the authors. My surveys show that, in general, a stumble means the text has not been tested with an actual, oral reading.
Here's the lesson -- You owe it to yourself, no matter what kind of writing you do, to read your work out loud at least once. It exposes errors, awkward phrasings, convoluted logic, and ambiguities. If you can get someone to listen as you read "final" copy, this is best. But reading the text to yourself, with a pencil in hand to correct or tick off problems to handle later, will substantially improve your prose in a fast, efficient way.
The biggest reason people don't read their text out loud is it feels like unnecessary work. It is easy to convince yourself that, if it looks good on paper or sounds good in your head, reading the text aloud is a waste of time. I have never found this to be true for myself or my students. People have argued with me about this, but I always win by having them read their "perfect" copy out loud.
For many people, it is uncomfortable to read out loud. Oddly enough, this can be true even when no one is around to listen to the reading. Having had nuns who made me quake as I stumbled through oral presentations, I have some sympathy for these people. Here's my suggestion: Read very quietly to yourself. It works.
I got this idea when I took a course with Danny Simon (the inspiration for Felix Ungar). He said his brother Neil would lean in toward his typewriter and read copy to himself before removing a page. Sometimes, he rolled the paper back in so he could make a change. Sometimes he just chuckled to himself.
One more tip: Before I read my text to myself, I let Alex read it to me. This is one of my Mac's text-to-speech personas and the only one I can tolerate. It is available via system preferences, speech, text-to-speech. (Microsoft has text-to-speech, too.) Alex is amazingly good at finding problems. I don't try to correct the text along the way as he reads. Instead, I drop in a Zen comment when I hear something that doesn't sound quite right. (That is, I have the reviewing bar open, move the cursor to the spot where the problem is, and click on the comment button. I do not enter text into the comment box because that would force me to pause Alex.) I go back after he is finished and fix the places I've marked. Since I put Alex to work, my own reads discover about 90% fewer errors.
Finding problems is what rewriting is all about. That's why, even though it sounds crazy, good writers need to make a habit of talking to themselves.