Electronic – Finding out the accuracy of the current probe’s measurement

Measure the AC voltage between PC ground, Scope ground and mains ground, using a multimeter.

Your PC or scope is probably floating, due to not being earthed properly to the mains, so you'll see half of the supply voltage from case to ground. This is inevitable, if there's no earth, stray capacitance and the EMC filter capacitors are equal between each line and earth. The maximum current is probably only a few mA, by law, but it hurts and it damages electronics.

Many a project has been destroyed by this sort of problem. I once saw it happen to a million dollar antenna's output amplifier, because of one cheap power plug adapter. So keep a bench ground cable and clip everything to it, before connecting up.

Keep in mind that anything adjustable will eventually require (re)adjusting.

The actual accuracy of a complete circuit has to take into account tolerance buildup; all the part tolerances have to be assessed. Certainly, an adjustable part (potentiometer in your case) can increase the accuracy of a circuit, at the expense of needing to go through the same procedure regularly.

Your 1% resistors will have an initial resistance of 1%, but over time and temperature, this is more likely to be of the order of 3% (I work in an industry where we support equipment for decades so such an analysis is important for us).

Sometimes it is worth adding circuitry to add an Automated Calibration feature that could perhaps invoke at power-up or on some regular basis, although that would be bit over the top for a simple resistive network. This is useful for high end test equipment, though.

The simple answer - yes, you can get better than 1% (provided your measurement equipment is better than 1%). The general rule of thumb is that to achieve a particular accuracy, the measurement equipment should be 10 times as accurate(but this varies depending on who you ask).