Mazda5: We thought about, but it was not commonly available in stickshift, nor in green (wife's prerequisites); reviews talk about road noise. Mazda's seem to have rust issues in these parts too. Might be kind of small with rear facing infant seats. Also, with the last row up you lose pretty much all cargo space.
Chrysler/Dodge Caravan/Voyager/T&C: Everyone talks about how bad the transmissions are, but I'm reading more about how they've either fixed them, or it's due to wrong transmission fluid (or never changing it). The 3.8's may drink oil, but otherwise the 3.3 and 3.8 seem to get similar mpg's. The 3.8's are likely found in the more optioned out versions. Not sure how old you want to go, but I'm guessing these can be bought cheaply enough used to allow some risk factor on the transmission. [I'm not sure I'm interested in "stow and go" if it reduces towing capacity; for myself, if I had a minivan I'd probably either always be using the third row, or never using it, so I would not be interested in paying extra for that option.]
RAV4: rearmost row is hard to get to, and meant for small kids only. Which might not be a problem; once they can buckle themselves in, little kids are known for crawling all over the place. They might even like it. Other SUV's seem to get similar marks for the rearmost row being hard to get to, and small at that. RAV4's may have issues with the V6 (which is timing belt); transmission whine (covered under a TSB, but might only be during factory warrenty--and is pretty close to a transmission replacement to fix) and water pump (not covered, and is a pain to replace--I'm sure OH can explain that better--and I'm pretty sure he has a low opinion of those V6's anyhow). The I4 model seems to lack that complaint, and is timing chain (at least on the '01-ish and newer); the 2009 2.5L I4 is rated better than the 2.4L '01-08 models (power, mpg) but all I4's use a 4speed auto (V6 was always 5 speed). No one seems to like the runflat tires on the Sport (or was it Limited?) but those can be replaced with standard tires. Also finding the third row in RAV4 is hard: it's not a common option for this model.
Odyessy: Some years were hard on the automatic, but supposedly that is fixed outside of those years. Don't know offhand what the bad years were. Sequoia's seem to avoid that common minivan transmission complaint. From antedotal reviews it seems the electric doors on minivans can be counted on to require repairs at some point. Personally I'd rather avoid them as a result (electric doors that is). Have not researched much into Odyessy/Sequoia beyond that, sorry.
I'm assuming the out-dated Astro and anything full sized is out of the question. I believe the larger SUV's can be had with 3rd row but again not sure if you are after those or not.