What to say about Mr. Finch? Well, um, he's…the absolute worst.
We know he's physically abused his wife and Finch for more than seven years. To add insult to (literal) injury, he left them to start a new family with Rosemarie and her seven-year-old son, Josh Raymond.
For the most part, our brief glimpses of Mr. Finch paint him as a stereotype. When we meet first meet him, he
[…] comes booming toward us from the backyard, where he's grilling thirty-five pounds of meat even though it's January, not July. His T-shirt says SUCK IT, SENATORS. (8.6)
There are, however, hints that there is more to Mr. Finch than meets the eye. Finch references his father's "black moods" (32.58), suggesting that bipolar disorder runs in his family.