A small jet uses about 40 gallons an hour. that means it the equivalent of 20 cars that get 30mpg. thats not much pollution at all, considering that just in the general area of your house there are thousands of cars but only a few jets.

From the reading I have done, jet engines release alot less polution than their horsepower equivelant piston engine. Not much exhaust at low altitude because they climb very fast these days due to noise abatement. I would worry if your house is inline with the end of a runway. People say there is carbon monoxide and engine exhaust, Im sorry but this stuff also comes out of any fossil fuel engine. I wouldn’t worry.

high crime rate outside of LAX !!!

I found this info: hope it helps.
Citizen Groups Concerned About Effects of Airport Noise and Pollution
Living near an airport also means facing significant exposure to air pollution. Jack Saporito of the U.S. Citizens Aviation Watch Association (CAW), a coalition of concerned municipalities and advocacy groups, cites several studies linking pollutants common around airports–such as diesel exhaust, carbon monoxide and leaked chemicals–to cancer, asthma, liver damage, lung disease, lymphoma, myeloid leukemia, and even depression.