[ohgom]

We just purchased a 05 Odyssey with 43000 miles. We had it looked at by a mechanic before purchasing and they said everything checked out great. So my question is what issues have people been having with this model?

It could be anything. But it is known for early transmission failure. After 2007 model, Honda started to use Ridgeline tranny. However, if you replace ATF regularly, you should be fine.