In a divorce case, when Findings of Facts and Conclusions of Law are signed by the Judge, but they have errors or false statements, can the requester respond and ask for more clarity? Does it serve a purpose to request?
You can do this.
If your goal is to ask the court to change its findings of fact or its legal conclusions, the mechanism would be a motion for reconsideration. If you simply want "clarity" about something that you think is vague, you can file a motion for clarification.
My understanding is that the odds for either motion would not be very good, though.
Besides that, it could be a bad idea to file such a motion. If the findings of fact and conclusions of law are part of a final order, it may be that time is running out for you to file a notice of appeal. If you work up a motion for clarification and wait 30 days for a ruling, it's possible that the court either ignores it or denies it, and waits long enough that you no longer have time to appeal the adverse decision.
I am assuming that you are referring to the reasons and findings the judge has put in the judgement, not things said in the courtroom.
The judgement is the judgement - it can’t be wrong (q.v.) because it’s the judgement.
However, if one of the parties believes that the judgement contains an error of law then that is (one of the) grounds for appeal to a higher court. If the appeal is upheld then the judgement will no longer (and never was) the judgement and a new judgement will be needed. An appeals court may write that themselves or refer the matter back to the lower court.
An error of fact is not appealable.
Unless the error of fact discloses an error of law. For example, the error is so egregiously unsupported by the evidence presented that no reasonable person could have arrived at that conclusion. Or, unless the judge’s reasoning is so crazy that the conclusions don’t follow from the reasons given - what’s known as “an error of law on the face of the record”. Something like this: