There have been reports of various transmission problems with this model.Google+
Car Problem Reports
Honda Odyssey Reports of Transmission Problems
Honda Odyssey Problem
Average Mileage: 114,800 mi (94,000 mi - 136,000 mi)
Visitor, 2004 Honda Odyssey, 115,000 mi
Transmission was slipping (high REMS, minimal power, spewing hot fluid which smoked on contact with engine). Initially, we had all the hoses checked, transmission fluid checked, drove adequately (but w less pick up) for a week, then same thing happened, check engine light came on, they ran the diagnostics, the transmission was toast, offered 2500 for trade in, or pay 5100 for repair.
Visitor, 2004 Honda Odyssey, 125,000 mi
Problem with the gear shift slipping. Repair shop referred us to a transmission specialist. Repair cost around $2200.
My vin # didn't come up with the recalled vehicles. Needed new transmission and all new mounts!
Transmission started slipping in drive and had to be rebuilt