Precisely what Cooper said. When using gradient alpha it determines what renders on top of what on a per-object basis (using their center point). In the current renderer, polygons within the object are not checked against each other to determine proper ordering.
Due to the performance cost many modern games still rely primarily on hi-res 1-bit alpha (mask) or on designing their assets such that transparency is not needed.
Looking at the screenshot there, I'd guess that the alpha is intended for the thatching hanging off the roof? You might try just using the mask alpha. If you can't get it clean enough, try using a separate material on just the polygons that actually need the alpha. That way you can use much more texture space in a second texture to do the alpha. This of course increases the performance cost for that asset, so use that technique sparingly.
The loss of collision is interesting though. What version of Maya are you using? Are you using the most recent version of the art pipeline? If you turn on "View Physics Data" in the physics panel, do the assets have a physics representation?
