For data communications the problem is often more complicated than DC resistance. Data signals are AC, and subject to impedance, (not simple resistance) inductance, and capacitance, as well as RF interference. A pair that's fine for slow on/off switching of DC signals may not be fine for higher frequency data signals.
You can also get intermittent shorts between wires in one pair and other pairs, even if the connection between the wires in the test pair are fine.
Back in the day I worked for a company that sold and serviced mini-computers to the US House of Representatives. The house offices would run serial cables up through walls and ceilings, and also under carpets. We had some flaky cables, and finally figured out that the offices would run the cables under the carpet, but over carpet tack strips. As people walked over the carpet, it would sometimes cause the tack strips to poke through the insulation, causing shorts and RF noise in the cables, which would mysteriously go away later.
Checking DC resistance will let you find breaks in your wires, but you can't assume that if the DC resistance looks good, the pair is good.
I would suggest using a simple voltage divider and one of the input lines on the Arduino for simple resistance testing, but that will only get you so far.
What you really want is a signal generator and an oscilloscope. You should send test signals (With voltages and signal patterns that resemble your data signals) down one pair at a time, and look at the signals on the far end, checking all the pairs. You should see your test signal come through, with the wave pattern still recognizable on the target pair, and no significant leaking of the signal to other pairs.