I was watching a video of a Japanese comedy show and at one point one of the comedians accidentally spilled a hot food on his superior. After that, his peers referred to him as "Tanaka-han" a couple of times. I figure it sounds like something mocking, but what does that mean, exactly?
はん is a name-suffix used almost exclusively by people from Osaka/Kyoto.
The level of politeness はん has depends on the speaker. Manzai comedians, geisha, or stereotyped heavy Kansai-/Kyoto-ben speakers in fiction may use はん everywhere, even when they're being very polite (e.g. お客はん, 社長はん). But I believe most real Kansai-ben speakers consider it as a colloquial and less polite version of さん, and use it sparingly.
Either way, it doesn't have any derogatory or mocking nuance. I guess you heard Tanaka-han simply because some people tend to speak in dialect when they're excited or want to make someone laugh.
It’s probably the comedians using Kansai-ben for さん?