Having worked in the utility industry for a while, I've actually been assigned to water bill discrepancies and requests at one time for a city I worked for. Concerning the meter being covered in dirt, there are two things that can be misleading here. As already mentioned, it could very likely be a "radio read" meter where it transmits the reading to a vehicle that simply drives by or a person who just waves a wand at it. Second, if you're in a sandy soil area and it's a visual read meter, the reader will remove just enough sand to read the meter and move one. One small rain storm will push the sand back on top of the meter, making it look like no one was there. Odds are though, now that the technology is more accepted and costs less, that it is a radio read meter.
Meters can and do fail, but they
usually fail in favor of the customer...meaning they will read less than what actually went through the meter.
Unknown to most folks, and even still un-believed by those shown the numbers and math to prove it, a very small pinhole leak or a running toilet (even one that only does it occasionally), can run up water usage deceivingly quickly. I used to have a little pocket reference card that showed the size of a pinhole and its associated leak rate/loos per month. If you've got copper pipes, the odds of this happening are high.
Here's a website that does an ok job of explaining common household leaks:
http://www.allianceforwaterefficiency.org/Household_Leaks.aspx
As others have mentioned, get in contact with the utility billing department and tell them that something is up. It'll be on your dime and time to figure out what is the problem, and they likely won't work with you on adjusting the bill until you prove that you've found the problem and made the necessary repairs to prevent it. Even then, don't expect them to wipe the bill clean. Water did flow through the meter and was consumed...even if only by a toilet or the ground in a leak. That potable water costs money to "make" (treatment is extremely expensive, especially sewage). Most utilities bill in a tiered manner, meaning higher users get billed at a higher rate. Usually it's so much money per unit for the first so many units, then a higher price per unit for the next block, and so on. If you can show that it was a leak and not just you being a water hog, they may be inclined to rebill all of the water at the lowest tier. That's what we did at the city I was at...and it seemed fair to me and most of the customers.
As someone mentioned already, go watch your meter when you think everything is off. There's a low flow indicator...usually a little triangle that spins. If it's moving when you think everything is off and not using water, then you've got a leak.