One problem related to sway bar has been reported for the 2001 Toyota Tundra. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2001 Toyota Tundra based on all problems reported for the 2001 Tundra.
I own a 2001 Tundra sr5 access cab trd pickup. I put 75,000 miles on it in through 8 ne iowa winters before moving to a warmer part of the country. My truck now has 132,000 miles on it. On August 17th, 2010 I drove through a pothole and heard a crack from the front left suspension. Upon inspection after work I found a busted left sway arm link. The link had rusted severely and sheared at the sway bar bushing location. I replaced the link myself with factory Toyota parts and torqued to factory specifications on August 22nd. I figure the new link will last at least as long as the previous one, but I'm guessing the right link is not in much better condition. Pictures and the what I have left of the old link are available. No injuries or significant damage occurred, but this could be a safety issue in certain conditions, and probably should be subject to a recall.