Reading the other comments, it seems that this is a somewhat standard practice to file at the last possible moment? If so, could there be a possible opportunity here for a software that files right before deadline making sure that mistakes like above do not occur?
Yup, and legal calendaring software is a medium size cottage industry in itself. It’s fairly standard, and that this firm wasn’t using something that automatically and verifiably counts dates and deadlines correctly is ... lackluster.
Many courts have allowed parties to file documents by email for years and federal courts have their own e-filing docket that (some federal district) courts mandate.