Unless you have a REAL crappy multimeter (for example with limited ranges), it’s probably accurate enough. The 8 bit readings in the Quad do not offer great accuracy, even when compared with cheap DMM’s. That’s why it’s important to calibrate it to get the most out of it. What the Quad voltage meters lack in accuracy they make it up for in bandwidth and ability to measure complex waveforms, while generally providing enough accuracy for most purposes.
Hardware calibration (high frequency compensation) is not in any way related to the DC software calibration. Doesn’t matter which one you do first.
If your device still has the clamping diodes at the analog inputs, I would strongly recommend removing these. Not only will these limit the voltage applied to the inputs, but if what you measure is of a low enough impedance (very often is) it can short the diodes and result in a dead channel, or even possibly blow a circuit trace and/or damage the circuitry you are measuring. The HW 2.81 device I purchased from SEEED had these already removed when I got it, presumably at SEEED’s request to their supplier. It did still however have them at the digital inputs.
I could go into a very long, drawn out discussion about the input circuitry of the Quad. I don’t wish to do that at this time, suffice it to say that clamping diodes at the input, without any resistive buffering is NOT a good idea…