Quote Originally Posted by Big Bri-dog
The first sentence means "I hope you don't mind my SAYING" (as opposed to my singing or my dancing), and the second means "I hope you don't mind ME saying" (as opposed to Chester saying or George saying). They are strictly different sentences in meaning, not different forms of the same sentence, I hope you would agree. Lots of people use the second form meaning the first form, which is strictly wrong.
*insert a direct copy/paste of Unne's diatribe in my LJ about how you can never say anything in grammar is right or wrong, which he used against me when I said something very similar about a similar error in grammar, and even though Unne was 100% wrong in that instance, I'm using it against him here in order to mock him*