My husband was recently terminated. He was given a corrective action form and one of the reasons listed was that he falsified a document. First of all, this is not true. Second, he is not aware of the incident that was mentioned as there was never any "formal" discussion or verbal warning per their records regarding this matter. Is there something that can be done about this?

Not legally, no. The accusation may have been unfair and even untrue. But even if the employer was wrong, this is not a wrongful termination under the law for which he would have legal recourse. A wrongful termination is when the employee is discharged for a reason specifically prohibited by law (such as because of age, race, gender, etc.) or in violation of a public policy. Neither of these situations appears to be true with the limited details you have provided.

I'm not so much concerned about wrongful termination as I am about the untrue accusations. Is there an appropriate way to address the issue so as not to have a potential "mark" on his certification?

What "certification"?

He is a certified nursing assistant. However, he was working as a rehab tech, not a CNA.

Not my area of expertise but if there is to be a "mark" on his certification, does this imply that there is some type of certification board to whom this alleged incident is going to be reported? And if so, that would seem to imply that for the sole purpose of the "mark" on the certification some type of review process could be requested.