I am very experienced in remixing poorly performed/recorded music. Below I've included three of my mixes I've done that were recorded badly. I've also used these mixes to demonstrate three different philosophies I employ when fixing a bad mix.
Method 1: The Whole Nine Yards
The first method I employed to fix up these mixes was to mix it to the absolute best of my ability. No matter how difficult. This means no sampling, and no re-recording.
Method 2: Cutting Out the Weak Links
The second method is based on letting go of what you don't need. Some of the drums were beyond redemption and so I replaced them with much better sounding samples. This allowed me room to let the mix breathe. The vocals also needed a lot of work in the tuning.
Method 3: Accepting Imperfection
The last method is forgoing clarity and embracing the imperfection as a trait of the recording. I distorted and saturated this mix to really emphasize the stylistic choice.