ToC via Styles formatting and Table of authorities - these are from the top of my head, which I remember not working properly with Open Office. They need to work when I do them and also should be displayed correctly when I receive them from colleagues in docx format.
Format painter, track changes, spell checker in two languages, intendation adjustments, page breaks, and paste as text - I use these like crazy but I don’t remember if they were OK in Open Office or not.