Since this is two months in a row, reading errors are not likely the culprit. The first thing I would check is to see is if the meter was turning with no water running anywhere in the house. If it is turning then you can start turning shut off valves on individual things to see if any halt the needle.
If the needle is not turning then some major water user in the home is not working right. Perhaps a toilet flapper is hanging too long and they flush a lot? Flappers like that can be tricky if they are hard of hearing. It might only get stuck occasionally but could waste a prodigious amount of water until the next flush unsticks it. Check to make sure the water levels of the overflow tubes are not very close to the top as well. If they are the valve might occasionally be trickling over for hours on end.
I assume they have no irrigation?
The meter could be wrong, but it seems unlikely. You could measure out some known quantity (e.g. 5-10 gallons) as a check of the meter. This will prove the meter right or wrong. All you need is some sort of calibrated receptacle. If it appears obviously wrong after such a check, then have the city check and replace it. I assume they would get some sort of credit for the months that are out of whack.
For perspective on the size of this discrepancy: my family of 4 is using a little over 3,000 gallons/month at present with roughly 40% of that coming from the 1.28 gpf toilets. That total is likely half the use of an average family this size, but in addition to the HET's we have low flow showerheads, a front loading washer, and an energy star dishwasher. (On the other hand, we don't eat out much and like to cook, which increases our water use for clean up.)
p.s. You did check that the days covered by the meter reading cycle are similar, correct? Sometimes we have a 25 day period followed by 37 days...with a predictable impact on monthly usages both in the short and long cycles. Convert this to a daily use for comparison.