Regarding the 2006 Odyssey, (or any Odyssey in general) there are 2 things to scrutinize:
1) Find out how many times the tranny fluid needed to be changed in the 120,000 miles, and make sure each one was done on time.
2) If they towed ANYTHING with it, RUN.
I can't stress this enough - you will have problems if you don't.
Look Here I have personally experienced this twice with V6 Honda vehicles.
As a side note, Honda started to use the heavier duty transmission out of the Ridgeline truck in the Odyssey around 2008. Still not perfect, but they do seem to be better. Just sayin'
