One problem related to trunk lid has been reported for the 2008 Honda Odyssey. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2008 Honda Odyssey based on all problems reported for the 2008 Odyssey.
Non powered trunk lift on my ex Odyssey just stopped working. I have to literally push the trunk and keep it in position and hold it, use the trunk and then leave the door slowly, without which the trunk door will slam on its own. I hear about recalls on this issue, seems like its applicable even to non powered models.