To answer the OP's question...
Air density varies with temperature and humidity. Power varies with air density. Higher density makes more power for the same reason your V's blower makes more power. Dyno readings are normalized for "standard temperature and pressure" (something like 72ÂşF at sea level), meaning the dyno corrects its measurement for the power gain or loss due to the variance in temp/pressure over "nominal". For example, if it's colder than 72ÂşF the air density will be higher and the engine will make more power. The "corrected" measurement will be lower because the Dyno is calculating what the power would have been if the air density hadn't been above "standard". Your corrected numbers are lower, so the air density at the time you did your dyno pull was higher than normal. Your car made more power than it would have if the air was at the standard temperature and pressure.
The Dyno reports the power measured at the wheels, which is generally about 85% of the power at the motor (the 15% loss is due to friction in the driveline and accessory system). You got 509.5HP at the rear wheels. Corrected, it was 494.5HP. 509.5/0.85 is 599HP, 494.5/0.85 is 581HP at the flywheel. So the numbers you're making seem to be pretty close to what they should be.
A K&N airfilter isn't good for much additional HP in my experience. Also in my experience, Mustang Dynos tend to read a little high. So while both the corrected and not-corrected FW HP numbers are higher than advertised for the V, that doesn't necessarily mean you're making any more power than the car made when it rolled off the production line... to know if you've gotten any gains, you need a baseline measurement prior to the mod, or you need a mod that makes enough additional HP that there's no doubt it's working.