Two problems related to noises during shifting have 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.
When vehicle shifts from 2nd to 3rd, there is a delay(grind). A and b pillars are week and produce a whistling noise starting at 35 mph. The rear bench (the bigger part of the split bench) will not latch down to the floor. Pax run flat tires are deflating with no age or puncture related problems. All of these are safety hazards. Rear lift gate struts failed and will not lift up rear door and can cause the door to crash down.
Had our 05 Odyssey ex-l in for standard servicing and was told rear and passenger side motor mounts required replacing (at a cost of $1200+)! van experiences noticeable noise and vibration as is shifts in and out of the eco phase of engine operation. I have never owned a vehicle that required motor mount replacement and after research, a service bulletin was apparently issued back in 2006 on this issue. This appears to be a widespread issue on the 2005 time frame Odysseys. This is clearly an engineering issue and should be addressed thru Honda via recall!.