For customer service and support, there are two considerations:
Some larger companies have found Twitter a good tool for providing support and have even set up specific support-orientated Twitter accounts. See the example below from AT&T's support account.
An important consideration for posting on Twitter is the tendency to post quickly without considering the implications or to respond differently from how you would if you were speaking to the customer face-to-face. Consider the following customer complaint:
An employee initially responded with:
After a backlash, the company tweeted:
Why do you think this series of tweets received so much attention?