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Our family is looking to purchase a used Honda Odyssey priced around 12- $13000. What can we expect for this and are there any issues we should be aware of. If this is not a realistic propostion would you please suggest a reliable alternative.

One thing the Odyssey is known for is poor fuel consumption. Also, transmission problems were not unheard of. However, if you need a people mover, they are great from a practicality perspective. As a generalisation, people movers are no longer popular new vehicle choices, with 7 seat SUV's being the preference these days, however, within your price range, if you have a need to carry a lot of people, they're most likely your best option.
Other models you could consider would be the Toyota Previa (or Estima), Toyota Ipsum or Mazda Premacy. The Mazda Premacy is probly the model that enjoys the best reputation for reliability.