From your question it is unclear what you want to accomplish. If your goal is to cause trouble with his current employer and get him fired, you may want to rethink that. A court will not get involved for that purpose and in most cases you will not be able to subpoena employment records - particularly if you don't have an active hearing pending. If you believe that it is important for his current employer to know why he was fired from his previous job, you can simply call them and tell them. However, you need to make absolutely certain that everything you say is completely factual or you may end up with additional problems.
Ultimately, you need to focus on yourself. If your marriage is over and you don't have children, you need to move on with your life. If you do have children, your ex husband's instability may be an issue in any custody proceedings and you may want to consult with an attorney regarding the best way to address these issues with the Court. It is a bit concerning that you phrase your question in terms of causing trouble with his new employer rather than addressing child custody with the court.
You can reach Harkess & Salter LLC at (303) 531-5380 or info@Harkess-Salter.com. Stephen Harkess is an attorney licensed in the state and federal courts of Colorado. This answer is for general information only and does not create an attorney client relationship between Stephen Harkess or Harkess & Salter LLC and any person. You should schedule a consultation with an attorney to discuss the specifics of your legal issues.
Sign up to receive a 5-part series of useful information and advice about child custody law.