limiting write-based per-day API access like the following way:
api-write-requests-per-day = floor(reputation/some_constant)
Btw. I don't think a 10k+ user would abuse the site from the API, although possible.
(the constant can be something from 10 to 200)
EDIT: some_constant can be different for different calls. asking questions, editing could have it set at 200 (so a 1k user can ask or edit 5 question per day), but upvoting, downvoting could be set at a lower rate, like 10 or 20. Commenting can be at 50 or so, etc.