I just got fired by my manager of 6 months at a Rails dev job I had had for 1.5 years.
For background, the person who managed me for the first year gave me nothing but glowing reviews. The former department head gave me a raise and approval to work remotely when I said I was having trouble making ends meet where I was living at the time. So I'm pretty sure I wasn't the problem. I was, however, the only employee working for the manager who fired me. So it was my word against his. He admitted that he was resentful of the fact that I had gotten approval to work remotely, and he and I routinely disagreed about the technical aspects of the work. In spite of that, I did everything he asked me to do to the best of my ability.
The organization (which shall remain nameless) is doing great work that I truly wish to see succeed. But the manager who fired me is a toxic individual who should not be in charge of anyone or anything. How do I effectively warn the organization about him now that he has fired me?
They have obviously already decided to take my former manager's word over mine in authorizing my termination. And if I go into the exit interview railing against him, the HR folks who will interview me probably won't take that very seriously.
So what would you do to convince this organization that the manager is the problem?
Effectively you are asking "how can I get the person who fired me in trouble?" I would step back and analyze your own motivations. Odds are, the situation is more complex than you would like to admit, even to yourself.
As for advice, try to figure out what lessons you can learn from the entire situation. Try to understand what really happened. Try to put yourself in your former managers shoes. Don't keep living in the past, and stop entertaining impotent revenge fantasies about 'warning the organization' about your former manager.