Personal experience after 6 years and 70k miles.
After picking up my new 2002 Odyssey at night from the dealer and driving it for over 30 miles, I found all four tires had less than 20 lbs of air pressure.
Excessive rattling noise from driver side sliding door - mechanics tried to take the door apart and gave up when they failed to remove one of the screws for the striker saying that it was the design flaw that cannot be fixed. They lost all door panel screw covers and never replaced them. I personally ordered them on-line and replaced them. When they broke the tip of large Phillips screw driver in the screw, they hammered and banged with chisel trying to remove it bu tin vane; left a mess. The problem was a loose sliding door with poorly fit rubber sliding door trim that failed to hold the door tight when closed causing the door's roller assemblies to rattle against the rails.
A/C hose broke within a year.
Heavy hammering noise from front wheels on rough road within a year. The head of the dealer service Dept. told me that they had replaced the front struts 0 which did not look new to me. When that did not improve the situation, I was told that is was a design flaw (that the calipers were loose) of the model and that it could not be fixed. The problem went away after the city fixed the street.
Wheel alignment problem from the day one - my Odyssey pulled hard to the right on freeway. I had to consciously hold the steering wheel hard to keep it straight. The dealer sales person said that it was a new safety feature of Odyssey to avoid head-on collision by pulling itself away from oncoming traffic when a driver dose off (?). The dealer mechanic could never figure out the reason. The problem went away after replacing all four tires.
Transmission ovverheating: A/T fluid turned very dark within 10k miles. The dealer mechanic said it was normal. I took it to a reputable independent local mechanic and had it serviced. I know when I see a burned A/T fluid. Later I received an A/T recall service letter from Honda for potential overheating problem. When I took my Odyssey to the dealer, they denied any knowledge of such recall and refused to help even after the service receptionist went to the office to verify. I had to return home to bring the letter to show. They finally found the internal memo regarding the recall afterwards. Even though it was a Honda's recall service the dealer asked for $80 plus dollars for test drive. When I refused they discounted half. Reluctantly I paid to get my Odyssey back.
Front door window regulator broke three times - twice on the driver side once on the passenger side. The first break down literally a few days after the warranty expired, the second a few months later, the last one last year. The irony is that I can hardly remember ever opening the passenger side window and maybe I would open the driver side window not even once a month in average.
The rear hatch door fell hard, almost knocking me out. Both gas springs for the rear door failed at the same time a few days before the warranty expired.
Both of my cigarette lighter sockets fell out. Again right after the warranty expired. I use them every few months.
Almost had a fire while driving. There is a 10-mile stretch of uphill driving on the way from Imperial Cty, CA to San Diego, CA. After driving to the top at between 3k-3.5k RPM, my Odyssey would not shift up to OD for about 10-15 miles. One day on my way to Mission Beach in San Diego, I saw a trail of a really heavy, heavy white smoke behind my Odyssey and the van began to slow down while the engine was spinning free at high RPM. I stopped on the freeway shoulder and opened the hood to find the engine drenched in some kind of oil. Some of it covered the exhaust system causing a heavy smoke trail. I drove it rolling down hill into a nearby gas station and waited until I was able to drive it again. I drove slowly back home and the next day to the dealer. The dealer mechanic could not find anything wrong.
A leaky A/C hose within two year. After replacing the faulty hose they forgot both caps, making me go back to get them back.
Passenger side rear window regulator stopped working right after the warranty expired. I got to use it maybe a dozen times in all.
The driver side front door panel trim fabric piece started to come lose even before the warranty expired. the rear driver side panel fabric just fell off some time later.