One problem related to steering wheel vibrate has been reported for the 2005 Toyota Prius. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2005 Toyota Prius based on all problems reported for the 2005 Prius.
Steering wheel started shaking while driving. Had wheel alignment checked, no problem. Took it to the ventura Toyota, they charged us over $200 and said the problem was loose screws in the steering column. This was quite scary and even though we had purchased bumper to bumper 100,000 mile warranty, this was not covered. They said it was only loose screws. We felt this was definitely a safety issue and if it hadn't been taken care of, we would have had steering failure resulting in an accident.