I bought GT5:P a couple of weeks ago. There is an update for the game, and it asked me if I wanted to download it. So I click yes and it starts downloading, but never gets more than a quarter of the way through before an 'error' occurs. I have tried so many times. 

Also, I downloaded the Grid and Overlord demo from the PSN Store. The demo's downloaded fine, but when I go to install them it never gets started because an 'error' occurs.

Has anyone else had this problem? What do you think is wrong and what should I do?

You should try and call Sony customer support, they'd be able to direct you to the problem without messing around from peoples suggestions (Not saying Suggestiond are Bad.)

Indeed, asking Sony Customer Service might be the best option to find out for sure. Though it sounds like an error in downloading than it has something to do directly with your PS3. Have you tried to empty the Cookies, Cache etc. memories?

I sometimes can't install games, I think it's because the connection drops during download, causing it to be corrupt. But don't quote me on that, I'm talking out my arse.

I haven't been able to download the GT:P update, either. Then again, I only tried it on launch day, so it may have been because it was busy.

Oh, and sometimes demos from other regions won't install, don't ask me why. But I couldn't install the Icon demo from the US store (not much of a loss, really).

The GT5:P update is ridiculously hard to download, it took me so many attempts. The others im not sure of, might just be a bad download. I wouldnt think its anything too serious with the PS3, but ring sony just in case.