It really depends on the bird. If the bird is one that spends most of it's time in perches, then I think you would have an easy time keeping an indoor pond clean (It would essentially be like an open fish tank) If it is a bird that spends most of its time in the water, then I think you would need some heavy, heavy filtration to keep the pond clean. Also, size would be a factor. Smaller ponds dirty quicker and may need heavier filtration. Where as a larger pond will also need more filtration for the larger volume.
I imagine you would do some neat aviary type things with small ponds in the aviary. It would just mostly depend on what you had in mind.