How to get KATE's Spell Checker to show all misspelled words?
I found several reports of this bug. Listing here, here and here.
However, there is a workaround. You need to disable Enable autodetection of language from Settings -> Configure Kate -> Editing -> Spellcheck tab.
Then it will detect the error if you go to Tools -> Spelling -> Spelling. But auto-detection doesn't work sometimes. You can make this menu a shortcut by using Settings -> Configure Shortcuts menu.