Twitter has its advantages for business, among them consistent, instantaneous contact with a demographic that chooses to be a part of the company's audience. Rather than mass market ads people are merely exposed to, ad nauseum, you can get specific product and sales information directly to your most motivated customers.
Twitter is great for being just that constant small reminder in the consumer's mind. It is like product placement in movies and television. Of course it could become annoying, but a twitter message is so short, and the people who follow twitter obviously like being "in the loop" with these short messages.
I think Twitter would serve the same purpose as an email subscription. You are consistently getting announcements about new products and ideas. As mentioned above, this is both an advantage and a disadvantage. I think the current advantage is that people are hooked into Twitter almost constantly. You have possible customers following you at any time, at home, at work, in the car, and while shopping. I think this would allow for quick response time to a good deal or the opportunity for businesses to create "quick" sales pitches for those already shopping. Would this possibly become annoying? Yes certainly, but frankly won't twitter eventually become annoying? =) I think a main disadvantage, other than that, would be how little information you could give out in a tweet. You would have to connect your tweets to your site where customers could find out all they need to know.
The biggest disadvantage I can see is that what might start out as interesting would become annoying. The same thing happens with e-mails. What begins as good deals and new information quickly turns to spam with overuse. While Twitter can be used in a few good gimmicky ways, the use had better be short.
Also, Twitter is just made for the catchy slogan or headline that companies can use to advertise their products. I guess that will allow them to share that to a wider range of people who can then find out more information about the product or company if they desire.
The major advantage for companies is that they can get followers -- people who are already inclined to like their products. When companies advertise to those people via Twitter, they are much more likely to get sales than they are when they advertise to the more general public. So Twitter ads are cost effective because they don't cost much and they are aimed at people who are likely to buy.