How many $\ce{^{14}C}$ measurements have been made?
How many have been validated by historic calibration, and what
  proportion (if any) yielded inconsistent results?


Often with an item that they want tested, a specific date isn't available so calibration isn't possible, but calibration can be done when dates are known.  Tree rings are most common and (though I've not read of this being done), samples from dead bodies from a specific battle or disease outbreak where a date of death is known.  Article here and here.

The calibration curve represents changes in the amount of C-14 present in the atmosphere which is also a factor.   There wouldn't be a charted curve if calibration hadn't been done quite extensively (see 2nd article above).

There's some room for bacterial or other contamination, especially with older objects, and contamination has lead some inconsistent results but that's not because the theory isn't sound but because of miss-handling.