One problem related to radiator 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.
My 2008 Honda Odyssey was completely disabled after running over a 1 inch rock on a paved road at 30 mph. According to the Honda service department who performed the repairs, the rock was tossed up by the tire into the undercarriage, came through the fan and struck the radiator from behind, putting a hole in it and stranding us in the mojave desert in July. According to Honda corporate there was no specific defect or design flaw and the "vehicle performed as designed. " Honda corporate also says that this could be a common occurrence with this chassis design but they do not keep track of such problems in anyway and only take any sort of action to address recurring problems when forced to do so by the NHTSA.