Good mixing and production won't save a bad song (what's colloquially called Polishing a Turd, excuse my crassness) but bad mixing can ruin a good song.
Casual listeners won't be able to discern that a song is "good" and that it's the mix that is bad. If one major element of a song sounds unprofessional, the whole song will sound unprofessional, and thus Not As Good as all the professionals they've been exposed to in the mainstream.
