".....I am wondering what the general rule is for manufacturers of wheel rims with respect to how eccentric a new rim can be...."
Each rim manufacturer will have its own set of RUNOUT tolerances. However, vehicle manufacturers have their own set of tolerances and the rim manufacturer will be required to meet those. These tolerances can be expressed in a number of ways, and usually they talk about "Composite" (Peak to Peak) and "1st Harmonic" (the best fit of a sinewave with one cycle to the actual runout trace - called the waveform.)
".....If a rim is marginally eccentric is the effect magnified at the surface of the tire. How much of an effect will there be on percieved balancing of the tire/rim combination?...."
In the radial direction (up and down relative to the vehicle), the rim and tire combine to form something different. In fact not only is there the tire and the rim, but the way the tire is mounted affects the runout of the assembly. Just last week I had a dealer mount a tire using very little mounting lube. He measured the result on a Hunter GSP9700 (which measures a form of loaded runnout) and declared the tire to be "out of tolerance". I asked him to lube both the rim and the tire, and try again. The result was an assembly 1/3 the previous value.
So in the radial direction, not only is balance not an issue, the real issue is runout (or as we tire guys like to call it - Uniformity)
However, in the lateral direction (side to side relative to the vehicle), runout does get magnified at the tread surface.
BTW, when we discuss the issue at the tread surface we usually express this in terms of a force - Pounds or Newtons. Rims on the other hand are expressed in terms of length - inches or mm's.
As a general rule, Lateral is not much of an issue with vehicles. Neither is Tangential (sometimes called Fore/Aft), but there are exceptions to both and I expect there to be more exceptions as vehicles get stiffer and lighter. However, Tangential is not applicable to rims - only tires and the assembly.
So balance is not the issue - run out (Uniformity) is!
But for a rim, OE limits are in the 0.004" to 0.006" range for the Radial 1st Harmonic. (The Radial 1st Harmonic is the one that really matters, not Radial Composite). If you use a Hunter GSP9700 machine, I'd recommend using 0.010" Radial 1st Harmonic, as this machine is not as precise as it could be.
I'd also use the same tolerances for Lateral 1st Harmonic. Again, Lateral Composite is not the one that matters.
BTW, the Hunter GSP9700 is preset from the factory with MUCH higher tolerances for rims and this results in bad rims being classified as "OK" and the assembly as "NOT OK", the conclusion being the tire is the problem. I'd recommend resetting the rim tolerances to about 1/3 of what the preset was.