Can I berate my coworker in public?
Why would you want to berate them in public?
Because they keep screwing up.
If you have problems with your coworker, you should berate them in private. Doing so in public might make you look like the bad guy to others.
I don't give a fuck what other think of me.
You aren't going to make them work harder by berating them. In fact, you might make things worse if you're overly negative.