Doctors are using Twitter to connect both with patients and other medical professionals.
Other doctors use Twitter to communicate with patients - generally not to give medical advice - but to guide the public to reputable sources of information, or share breaking medical news. The CDC, for instance, uses Twitter to provide constant updates on H1N1 influenza.
Finally, Twitter offers an opportunity for doctors to ask questions of other medical providers. Given the real-time nature of Twitter, opinions and answers to clinical issues can be obtained immediately.
Some doctors simply do not have enough time to Twitter, or utilize other social media applications like Facebook. And time spent with patients in the social media sphere is not compensated by health insurance.
But Twitter is a valuable way to reach thousands of people at once.
My opinion: I was a Clinical Assistant Professor of Medicine at CWRU until 2008 and I think it is great that the university community shows an active interest in social media services such as Twitter. Using Twitter frequently @DrVes, I follow 77 accounts and have around 3,500 followers. That said, I am yet to ask medical questions on Twitter and generally do not answer clinical queries from patients there.
Assistant professor uses Twitter to teach students dental anatomy at Ohio State University - 113 of 200 students signed up, 56% http://goo.gl/jvyq7