Appeal is one way. Another is to try to point it out in your papers. Motion for reconsideration or clarification may be allowed. I dont know under Il law. Practically speaking, I think it unlikely that every judge reads everything submitted. Many judges have research clerks/attys who read and research. Some are just overworked, and some are lazy. Some read a portion, and when they think they have what they need to make a ruling, they may not read more. being able to prove that is unlikely. Welcome to the world of lawyers. I have had a judge make a ruling on a motion based on grounds not raised by the other side in their papers, and never raised by anyone at the hearing! It read like a brief advocating for the defense. It was a case against a school district. I learned several years later, that this judge had worked defending school districts prior to his appointment to the bench.
A judge's ruling is scrutinized by the appellate court if either party questions it. Judges read or listen to evidence. They do not generally make sua sponte observations or decisions. It is up to the attorneys, or the parties if pro se, to bring the proper motion in order bring something to the court's attention. What you characterize as malpractice is probably more like an attorney failed to bring something to the judge's attention.
I agree with my colleagues. You have two options. You can file a motion for reconsideration pointing out those facts in the record that the judge overlooked, or you file an appeal and make the same argument to the appellate court.
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