If the "mess up" is deliberately discriminating against somebody over a protected class like sex, I think firing them immediately is a fair and arguably ideal action to take. I would be surprised if this wasn't the standard operating procedure in most companies.

I assumed from the phrase "massive jackass" in your post that cruel behavior from him was typical and dramatic enough to be a marked pattern. Most companies /are/ willing to fire people who repeatedly disrespect and are cruel to their coworkers. It's part of a bare baseline that you need to maintain to have a decent work environment for your employees. You and the woman he discriminated against makes at least two separate eye witness reports to an egregious offense (protected class discrimination), and I assumed from your description of him that his cruelty wasn't just exposed to you two.