For the DMMCheck Plus voltage and current measurements, the probes or clips you use do not matter, for the reason I proved earlier using Ohm's law. You can put a decade resistance box in series with your DMM and crank up the resistance to see for yourself. A common resistance to encounter when using test leads/probes/etc. is going to be under 1 Ohm, typically around 0.1 Ohms if you're shorting them directly. The contact resistance would have to be very high such as 100 Ohms or more to be an issue.
However, for resistance measurements, YES, the type of probe and lead you use and how you hold it makes a big difference in a 2-wire configuration, but the accepted solution is a 4-wire/Kelvin connection.
Soldering on the reference invalidates the calibration, and there is just no way around that. Will all the values be different or "wrong"?? That is up for speculation and it would really require another calibration with an 8.5 digit DMM to "know" one way or another. But again the fact remains the previous calibration is no longer trustworthy.
The 34450A is not a good enough DMM for analyzing the performance of the DMMCheck Plus. One year 10V range accuracy spec is 0.015% reading + 0.005% range. So 5V could display between 4.9988V and 5.0013V.
However, I've commented before on applying too much value to published specifications, so without the calibration data we shouldn't speculate too far on the actual performance of this 34450A.
But comparing the before and after measurements, and given the performance class that the 34450A is targeted for, it would be unwise to put much trust into the last digit of the display regardless.
I recently received my DMMCheck Plus back from calibration:
34401A: 5.000,00V
34461A: 4.999,98V
K2010: 4.999,995V - 4.999,997V
For verification, I also got identical readings from my PDVS2mini @ 5V.
For 1mA DC, my calibration sheet states 1.0009mA and I observed:
34401A: 1.000,94mA
34461A: 1.000,863mA
K2010: 1.000,779mA
I would put more stock into the value provided by the 34461A since it has a 1mA range while the other two only have 10mA.