What is the black residue on my pans?
The answer is polymerized oil - which is the same stuff that is built up on cast iron skillets during the seasoning process (although this is problematic and undesirable on non-stick pans). Further, it's very hard to clean once it's set in. Lye can be used to clean it but you must be very careful with it. The residue occurs when oils burn at too high a temperature (you should be able to tell this is occurring by watching for the oil starting to smoke).
The residue does not cause any safety issues. For better or worse you can simply think of it as part of the pan.