I also noticed that the larger the file size became, the longer the game was taking to load initially from the starting screen, and would do the same when I would try to save in game. I hit the "x" button and the game doesn't respond for several seconds, taking longer and longer to bring up the save menu. Now it's building up the the ten second mark and I know this will only become worse with time as well.
My assertion is that Skyrim for the PS3 is an inherently broken game, with glitches and bugs far worse than what can be patched. The more you unlock, the more impossible the game becomes to play. I had these very same experiences with Fallout 3 and these problems were never fixed. Once I hit about 13MB on Fallout, the game would lag to the point of freezing in the open world and made combat impossible.
I can't say for sure if it's just a compatibility problem with the engine running on the PS3, or if the PlayStation 3 just isn't powerful enough to handle such a massive game with ever increasing save file sizes. I can't imagine anyone not having problem with this game either in quests being bugged to where they are unplayable, or the inevitable lag-death that seems associated with Bethesda's games on the PS3.
I will say that all in all before I started experiencing these problems, Skyrim was one of the best games I've played in ages. Heck, I'm even going to get the game on PC once I can afford to upgrade.
I will not purchase another product by Bethesda for the PlayStation 3. Fool me once, shame on me and so on.

From my experience the PC version is fine.