Should be fine, although I'd say not to use shared passwords between twitter & other sites just as a second level of safety.
No doubt about is about Twitter safety. If we compare it with Facebook then Facebook is better than Twitter according to safety.
Safe? Seems to me that a twitter account is so transitory for most people that it does not have any real value. Just occasionally use one of those twitter tools to save a list of follows and followers in case your site is hacked or suspended!
I too think its safe.And you can be more safe by using private browsing while using twitter or other sites