Twitter's 140 character limitation removes lends itself to more of a customer relations tool than a marketing channel, and is better for "raw customer interaction."
Should you dedicate staff to monitor Twitter? Sure, but make sure your Twitter champion understands the etiquette of social media (Todd commands you to read the Cluetrain Manifesto or you're not going near a brand's social media campaigns).
The big brands who are engaging on Twitter are the ones that have already made customer service a priority for their business. Companies like Jet Blue, Southwest Airlines and of course, Zappos.
Twitter is kinda/sorta like an offline live chat for customer service in the sense that you can conduct customer service and 2 way communication through it. Plus it's free. (Linda's comments: I don't think there is a comparison as there can be huge time lags between "tweets" and you are painfully limited to 140 characters. Plus, it's all in the open (unless you private message) which has both pros and cons to it. You can't use it as your only customer service channel but it can be a great reputation management tool - a shining example of how open and helpful you are.)
Michael suggested using services like Summize or TweetBeep which taps into the conversations around your brand. You could have someone check in 2-3 times per day.
Big companies are often afraid to open the floodgates on social media in case people say bad things about them. What they need to realize is these conversations are going on anyway so you might as well get your head out of the sand and listen and respond.
If you're going to use Twitter, keep your sales tweets and customer service tweets separate. Some people will want to get your deals, some your customer service - don't mix the 2 or you'll turn off those who don't want certain messages. If you're doing sales promotions, unique and time-limited deals can work well.
SEO and Twitter? It can be a good reputation management tactic. For example, Barack Obama's Twitter page is #4 for his name. (Linda's tip: link to your Twitter page from your store domain to boost the Twitter page's relevance, and any other blog or social media profile you have).
Todd says, if you build up a good following, down the road you can push some markety stuff and you may just get some links out of it, or be able to leverage your Twitter account for social media marketing.
Affiliates Who Twitter
I came across a couple affiliates who use Twitter to promote Wii - WiiTracker (79 followers) is one, but even cooler is WiiMe. WiiMe uses Amazon Web Services to pull data whenever the Wii is back in stock. 597 followers are alerted whenever the Wii returns to stock, and alerted when it is sold out - often in less than 15 minutes!
I think Circuit City should start one of these Twitter accounts. (Be your own affiliate!) I keep getting emails from Circuit City about the Wii, and when Wii comes back in stock. Having both avenues for communication serves 2 different ways that customers like to be contacted. Especially for tech-savvy people who get mobile Twitter updates. The callout to subscribe to back-in-stock updates by email, RSS or Twitter could appear on the product page. Just a thought.