On meters for electricity...
Having been in the business of just that (just before "smart" meters appeared on the scene), There are lots of things some people might not understand. Those rotating dial meters that frequented homes for the last century are pretty accurate. While it HAS taken a while, over time they have become better at their job. The first "smart" meters (I had one) that had separate registers for various times of day, were simple detectors of the rotation of the disc that was driven by voltage on one side, and current on the other. So, if the mechanical meter was "wrong" (or "right") it would continue to be, it just was counted a bit differently.
The typical meter on the side of a house (here in the USA) was a "Class 200" one that was good up to 200 amps at 240 volts (we commonly use a center tap to get to 120 volts). The relevant standard of accuracy (ANSI C-12, if you want to look it up) was to have 1% accuracy at 1% of full scale, so you needed ti be accurate at about 20ma of current, which isn't that much.
What made things more fun was that if you want higher currents in your house (are you powering a VAX??) you could ask for more and bigger conductors and a higher class meter were put in place. These higher class meters typically used current transformers to take the max (say 320 amps) down to something more reasonable (like 3.2 amps) in a 100:1 ratio coil. The fun begins when said current transformer gets a DC current impressed upon it and saturates. A simple way of doing this is to have a nice fat diode in series with a space heater, and you turn it on, and watch the meter come to a screeching halt. I suspect that the metering method that needs to integrate to get the current signal will have the same problem, but can be fooled wither way. A large spike in the wrong direction for a brief instant (very easily done with a spark or three) will really foul things up.
Metering electricity is pretty tricky, and can be subject to all sorts of ailments. One old trick was to squirt sugar water near the meter and wait for ants to get into the inside of the meter and foul up the spinning wheel (it doesn't take much!). This was solved when insecticide was put inside the breathing hold cloth spacer to thwart such things. So, people can become VERY inventive when it comes to absconding with power, and sometimes to just doesn't work out. You need to test for LOTS of possibilities. Any metering company that hasn't is asking for trouble!