One problem related to tire blowout has been reported for the 2005 Honda Odyssey. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2005 Honda Odyssey based on all problems reported for the 2005 Odyssey.
Aug 2008, purchased 4 versado lx tires at 46851 miles. On 14 Aug 2011, had a tire blow on right rear on I-16. There was $75 damage to car as the tire tore the factory mud guard from the fender. Tire was replaced for $53 under warranty at 77968 miles. On 10 oct 11, returned to dealer and found 2nd tire separating. Replaced for $73 under warranty at 79720. On 23 may 2012, 3rd tire was found to be separating at 84275 miles. I contacted toyo by email. Rep called my local tire dealer, raffield tire, and discussed issue. Dealer was told to reinspect 4th tire closely while replacing the 3rd tire for $83 under warranty. It appeared to be ok. On 3 Jul 12 the 4th tire was replaced for $79 under warranty at 85676. Had long discussion with toyo customer service. Was told there were "no known issues with this tire". Very funny that all 4 tires for my vehicle failed. Tire dealer does rotation/balance/check every 5000 miles. Wanted toyo to replace this tire at their cost due to all of the trouble I have had. Rep refused, stating that the government would not let them do any customer relief other than the limited warranty on tire. Otherwise, "they would be guilty of hiding defect information from the government". I cannot believe there are no known issues if all 4 of my tires failed. They also could not pay for the repair I had done in Aug 2011 since the tire was not turned over to an independent 3rd party for analysis.