The smoothest planet in the solar system is probably, AFAIK, Europa. It does have plate tectonics, of a sort, but it's ice plates floating on a water ocean. In terms of habitability, not great. Also, smoothness is here defined as maximum deviation from ellipsoid, not how steep those deviations are. I recently read (I forget where) that it might have fields of knife-like ice projections (which have a name that I also forgot) metres high and quite impassable.
Since you're probably looking for something more earth-like, I would guess that you can't avoid mountains. To develop complex life, you need a healthy mix of elements on the surface, plus a reasonable protection from radiation. You get the first from tectonics and volcanism, and the second from a molten ferromagnetic core that provides a magnetosphere. You also need surface volatiles (water, atmosphere) which in Earth's case got there from cometary bombardment, if memory serves. Someone correct me if I'm wrong.
Finally, I would think that thermodynamics on a flat planet would be too bland. We have no idea how life got started (ok, we have too many ideas), but what is sure is that you need an mixture of gradients: one chemical species diffusing from A to B, a temperature gradient going in a different direction, a liquid current carrying everything the third way etc. That is why all models of biogenesis, starting with Darwin's warm little pond are on some kind of interface. If the planet is too flat, I suspect the conditions might be too uniform. I haven't checked this suspicion in any way, and I doubt anyone has, so it could be completely wrong. But I have a hunch.
Of course, you might not want life to develop there, just to be able to terraform and settle it. In that case, apart from probable lack of magnetosphere, I don't see any objections. Your ecosystems might be a bit boring, though.
An idea that might work: take an old planet around an old sun, and make it the only planet in the system. You could have a red dwarf that got too close to some energetic young suns and had the rest of its planets stripped away. Leave a circum-stellar dust ring that provides just enough micro-bombardments for any mountains to be eroded to low hills.
Now you have the right shape, but you lack water and atmosphere. No problem: the micro-bombardment has gradually shifted the planet's orbit outward (would that happen? Um...) and the outer layers of the dust ring are water-rich (which would happen). So a layer of water accumulates on the planet. Take it from there.