Thats easy Matt, if an intermittent issues were the problem, then his meter reading would reflect that and confirm that his overall average consumption in that time span was lower than expected.
this would then enable you to look for causes responsible for a lower reading which could be as you said an intermittent connection, or a faulty thermostat, I would hate to find an intermittent connection on a 3Kw heating element as that would be a recipe for fire!
But if you are using the consumption to ascertain the wattage of the immersion then how do you know what to "expect" Mike?
we should be expecting readings closest to the nearest industrial standard wattages available for these elements, 3kw being nominal, so we would expect to see a reading of his consumption very close to a quarter of this as the test duration is for 15 minutes and in that time we are hoping the element stays on and not get switched off by the cylinder thermostat , so we need to make sure that the water is not hot already in the cylinder.
(as well as I assuming the mains supply voltage is around 230V, I remember how about 15 years ago, in my home I started getting 198V! all my florescent lighting wouldn't start often, and other lights appeared very dim, I had to report this to London Electricity, (LEB) they came and placed a plotter for 24hr monitoring and when they investigated the cause, it transpired that they there were two Main street fuses one on either end of the street, so one of them had gone off, causing only one fuse to feed my entire street! Strangely i was the only one who complained they said, that is because i happen to have a DVM, so I checked my voltage and was alrmed that it was so low!
After they restored the 2nd fuse, my power levels rose to around 220V to 230V. (Streets are wired like a grid work, mains being fed from either end, and I guess if you lived in the middle you would be getting less voltage than your fellows near the ends.
Matt, I am not trying to be smart here mate, just the fact that many people who come on here to ask such questions wouldn't need to if they were capable of owning and using a multimeter or a clamp meter, they would have already carried out their own test and eliminated any doubts.