Non-compliance issues are typically if one: exceeds the [age length limits, uses a wrong typeface/font or size, exceeds a margin requirement, doesn't conform to the cover sheet style, omitted page numbering (if required), or any of a dozen or more other formalities. Each jurisdiction has its own rules. For appeals, many jurisdictions require one party to use a red paper for the cover sheet and the other party to use a light blue paper for the cover sheet (if hardcopy is required in addition to electronic filing, which it can be in certain jurisdictions, and bind the briefs in a certain manner.
Most professional quality litigation teams have a junior associate and a paralegal assigned to review all filings before they are submitted to the court so these non-compliance issues don't happen. The associate and paralegal must review for cite-checking, typos, any other writing issues, and to ensure that the document complies with all the rules and requirements of the court to which the submission is to be made.
Getting a notice of non-compliance is an embarrassment and usually means the lawyers are sloppy and don't have a good pre-filing review process and/or they rushed to meet a filing deadline and didn't do a review at all. Bad form.
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