What must still be written by hand

Three places, and this application deliberately leaves all of them blank.

On the 身元保証書 (letter of guarantee), the guarantor's name is marked 氏名（自筆）. It is a signature field. A printed name there is a common reason the document is handed back at the counter.

On part 3 of the application form, the declaration carries the applicant's or representative's signature, and the form's own note states that the date of preparation must also be written by the applicant in their own hand.

The form additionally says that if anything changes between preparing the form and filing it, the applicant corrects it by hand and signs the correction -- so keep a pen with you at the counter rather than reprinting.