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Diving a bit deeper into what I wrote earlier. You can derive from Doug Rytting's presentation (see above) or from the signal flow graph that the uncorrected reflection Γm measured by the VNA for a DUT with an actual reflection coefficient of Γ is Γm = e00 + (e10e01 * Γ) / (1 - e11 * Γ). When the VNA assumes an ideal load during calibration (Γ = 0), it follows that e00 is determined during directly from the calibration measurement Γm of the load. Therefore, the error caused by an non-ideal load is (e10e01 * Γ) / (1 - e11 * Γ).

Now, you might rightfully point out that you're not interested in the error in e00 but in the error in the measurement of the Γ (=S11) of a DUT. That's unfortunately not so easy to write down because it also depends on the reflection of the DUT itself. As Dave stated above, the non-ideality of the load must be significantly less than the S11 of the DUT you want to measure.

To show this better, I dug out my VNA simulation (MATLAB script) that I wrote a long time ago - hoping that I didn't make any errors back then ;-). Here, I simulate an ideal VNA, i.e., no errors in the VNA itself, since we're only interested in the errors caused by a non-ideal load. Furthermore, I simulate a calibration where the VNA assumes the load to be ideal, while it actually isn't. From the attached plot you can see the error this causes in the S11 (= Γ) measurement of a DUT, depending on the actual S11 of said DUT and the actual reflection of the load.

Some notes:
- I only investigated the error in the magnitude of S11. The phase is of course also affected.
- When measuring for example the return loss of an antenna you might not care whether it's exactly 20 dB. Hence, you might be able to accept a higher error caused by the non-ideal load for low reflection / high return loss.
- As already mentioned, if you know your load standard (i.e., its Γ) you can correct for it and the measurement error will be much smaller; basically just defined by error/uncertainty in your load standard definition.

Regards
Christian