Depth precision will improve with future drivers, as far as zbuffer goes.
At current, 24-bit zbuffer displays artifacts in just about everything, just your average Joe doesn't really notice it that much. 16-bit zbuffer is totally broken, as a quick round of Half-Life, Quake3 or even most D3D games in 16-bit will quickly indicate. Decals and the like are showing through walls completely in 16 bit.
Funny thing is, this isnt much worse than the zbuffer artifacts early on with the GF4. They fixed this, although it still has a handful of zbuffer errors/artifacting left (missing trees, polys in the distance that dissappear/reappear, etc.etc.).
It just goes to show that all the newer zbuffer/occlusion technology likely has a big impact on the complexity of driver development given the bazillion different software titles out there. Adding additional depth precision comes in time, but usually has some cost in terms of performance. Seems IHV's would rather schmooze through faster benchmarks on product launch with less than perfect depth precision... and add precision later once other performance optimizations are found to help "balance out" the toll taken by fixing these issues.
That's my opinion anyways. The single most important thing to an IHV at product launch seems to be 3DMark and Quake3 scores, the second most important thing is releasing drivers to the people that rushed out and bought these cards due to those scores that do not drop them, while at the same time fixing things.