After Quagmire gets strangled into unconsciousness, his feet are shown close together. When his body is shown from above, his legs are suddenly far apart.
When Quagmire gets in the car and hits the gas, his tires squeal even though the car is on a dirt road, not asphalt.
It makes no sense for Joe to have just moved on and continue being friends with Peter after he put Joe's eye out with a BB gun in Lottery Fever (2011).