Well, bad paint isn't going to turn brown. Bad clear coat can turn a yellowish color, but odds are something is building up there.
Don't use dish doap on paint. It'll speed up oxidation. Just, no.
Swirls and scratches are not from bad paint either, they're from bad washing (no offense). Drive through car washes are likely the cause of those.
Professional detail would probably do wonders for your car.
2014 Mustang GT Premium 401a; "Now you can add Premium to your signature." - Thereaper