The symptoms of a bad air filter include poor acceleration or increased fuel consumption, unusual engine noises, check engine light, misfiring, decreased acceleration, sometimes black smoke from the exhaust and reduced engine performance.
If the air filter is really clogged then the clogged or dirty air filter can cause your car to jerk as it can restrict airflow to the engine and hinder the combustion process although a dirty air filter is not the common causes of a car to jerk but it can be a cause of car jerking.
A vehicles air filter ideally should be replaced at least once a year or every 12,000 miles or more often if you do a lot of driving in dusty conditions.
A dirty air filter can reduce your fuel mileage and cause poor performance as the engine cannot get the air it needs to operate.
I always replace my engines air filter on my vehicles every year unless it gets dirty before then.
A new air filter is pretty to install and are often not all that expensive either.