The whole plot device of Gordon conveniently writing out a full confession that he decided not to say (but is perfectly fine mentioning to a large audience) is ridiculous.
It is odd, for sure, but nothing that brings down the movie in my opinion. For all the audience could have known, the "truth about Harvey Dent" could've been most anything, and seeing how this was only a small gala event it wouldn't have made too much of a splash for him to mention it as a passing comment.
That slight mention of the letter in Gordon's speech at the Dent Day event was supposed to represent how he so eagerly wanted to tell the audience, and against his better judgement could barely hold it in.