This is a point of great contention, with different sites grading different profanities to different levels of 'swearyness'...
Back in 2009 The Magazine TOTALFILM claimed that Casino held the title with 398 F-Bombs, at a rate of 2.23 per minute. This was apparently enough to make it into the Guiness Book of records.
Since then however, certain films have been re-appraised and other contenders for most fucks have been entered.
Wikipedia lists the contenders here.
The highest count now belongs to a documentary called, aptly; 'Fuck'. The word is used 857 times, at an average rate of 9.21 fpm (fucks-per-minute).
The highest use in a fiction film belongs to the cult slasher Gutterballs, with 625.
Closely behind it is the very recent The Wolf of Wall Street, with 506. Certain Newspapers erroneously claimed this to be a new record.
However, if you factor in the running times of Gutterballs against The Wolf of Wall Street, you realise that Gutterballs packs in three times as many swearwords per minute, making it pretty unbeatable...or should that be, unbearable?
EDIT: Here's one for the Conspiracy theorists amongst you! since someone posted a comment correcting the article in the Independent, the Gutterballs entry has been removed from the wiki-link! interesting, considering anyone who has seen it can definitely vouch it has more F-Bombs than The Wolf of Wall Street.
I wonder if Scorcese's people have leaned on wikipedia to hide the truth, so they can claim the soundbite-friendly prize, or if there is some genuine reason why it would have been removed? Maybe migrate this to Skeptics, ha ha.