Doing a quick test of funny characters:
Accented áéíóú àèìòù âêîôû äëïöü (entered using UK Extended keyboard layout in Windows)
Other random characters ÆĄĐߍ€∫ (entered using Windows Character Map)
Unicode à (entered as hex - doesn’t work)
Unicode àáâãä (entered as decimal - works)
Named HTML characters αβγδε (entered as α and so on)
Superscripts ¹²³ (entered as ¹ and so on)
Superscripts ⁰¹²³⁴ (entered as decimal unicode)
Mathematical symbols ∀∂∃∅∇∈ (entered as ∀ and so on)
For Windows PCs, it looks like you can get most characters using the built-in character map (not installed by default, but usually easily added). Beyond that, if you know the HTML 4 character name, you can use that and failing all else, you can use unicode, but it has to be in decimal not hex.