Can electrical surges cause the meter to spin faster causing huge electric bills?

The power constantly shut off and on the current in our neighborhood, can this trigger faulty reading on the meter.
Thanks

Yes, but it's not a faulty meter. Motors and inductive loads draw a lot more power on startup than when running. Those surges in consumption are counted.

When the power comes back on the resultant surge will momentarily cause a spike in your wattage usage, but this would be minimal,lasting a second or two. I doubt you would be able to see the effect on your monthly usage, even if it happened several times per day. And meters are pretty accurate - I don't see how a spike would cause the meter to "spin faster" than it should.