You should still have a way out of this. But it certainly makes you vulnerable. My recommendations -
1. Accept that you made the mistake.
2. Make sure you understand what you did wrong that led to that mistake. This means not just accepting "I did mistake X" but also understanding "I did Y and Z which led to me making mistake X".
3. Make sure you understand the remediation plan you have been given. What do you have to do to meet the remediation? To whom do you have to prove that you have met the remediation? What evidence do you have to provide to those people which will persuade them that you have met the remediation? What is the timescale, both the final deadline and any intermediate goals? If you are unclear on any of this, talk to the relevant people to clarify it all now.
It might help you to set all this out in a table, with the answers alongside these questions, and clear it as a proposed course of action with those who will be judging you on the answers.
4. Keep track of your progress, keep talking on a regular basis to the people judging your progress, and make sure that they are kept up to date with the evidence you will be compiling that you are satisfactorily working through your remediation issues. By the time you come to the end of your remediation process you and everyone else concerned needs to be fully aware of what you have been doing, and have a neat pile of evidence of how you have met the remediation.
The short form of this is "You have an extra training course to complete in order to continue your residency. Make a plan for completing it, the way you have made plans for getting through earlier courses and exams, and then implement that plan."
If there is a resident adviser, trade union official, or similar person attached to your program who will be on your side rather than the side of the hierarchy, ask them for help.
I'd record everything everyone says to you. Buy a cheap little mic recorder/mp3 player and a 16GB microSD card from Best Buy and carry it around everyday in your shirt pocket. At the end of the day, transcribe and date the conversations and save the sound files on your home computer. Save a backup in a hotmail or gmail email account, not the hospital one.
"Remediation" plans either mean that they are trying to remediate a deficiency, or they are trying to set the groundwork to can your ass. If it is the latter, having a consistent record of the interactions you had with your superiors and coworkers may be a valuable asset come lawyer time.
This is also illegal in many states unless you have their permission to record your conversation (although it is legal in some states so long as you are part of the conversation). It may also cause HIPAA issues if you capture patient information accidentally.
Are you guys serious?! You think a busy resident is going to have the time/energy to edit 12 hours a day of recorded audio? Residents mess up. Learn from the mistake and move on with your career.