Sounds like they're stuck in one of those bad mentality loops: "Nothing works, things will never change, woe is me!" A bunch of Eeyores straight out of the Hundred Acre Wood. Welp, now's the time to let them all know there's a new sheriff in town. Start with a review of the past records, making copies of the incorrect forms and come up with an idea of the trends. You can bring all the staff responsible for MD into a refresher training and let them know the errors you've spotted. Remind them of the SOPs related to MD monitoring as well as the proper way to fill documents. Let them know the errors are unacceptable, disciplinary measures will be taken, and possibly consider replacing MD staff with other production employees who show initiative (once you've gotten to know some of them better).
If your plant is like others I've seen, the staff trusted with CCP monitoring typically receive a slight promotion for doing this job. This is because the job is serious, and the company expects more out of these employees. If that's the case at your plant, then make them earn that position and keep earning it. Lastly, you'll probably want to be on the floor during this new period a lot: show up at the MD when a check is to be performed to watch how it's done, show up between checks to verify the records are up to current time, making them correct errors on the spot and document it for performance reviews.