Witnesses. Some documents require one or two witnesses in addition to the notary. Illinois does not let a notary serve as a witness on the same document, so line those people up before the appointment.
Missing notarial wording. Plenty of forms come without a certificate. Illinois allows a loose certificate to be attached, and the correct acknowledgment or jurat will be supplied on the day.
Remote signers abroad. Whether an overseas signer can be notarized remotely depends on what the receiving office will accept. Say where the document is going when you call, and it will be checked before the appointment is set.
Documents in another language. The signer must be able to read and understand what they are signing. If a certified translation is needed, that happens before the notarization, not during it.