I can't install the latest version of the Maxis patch, which means I can't install Uni.

I've removed all hacks and user-created objects from my downloads folder. Any other suggestions?

You don't need the patch if you are going to install Uni. Just go straight to installing the EP.

I heard the one on the Maxis site now is the new patch, not checked it though. If you've done all that already, I'd just uninstall it and reinstall it, it doesn't take long. I'd make a back up and copy it all too just to be safe. Read the info on this in the Help Section.
I think you do need the second if you already have one, Uni just puts the patches on if you havent any at all.

I do. It tries to install the patch on it's own at the end of the Uni installation. It then says there's an error. So I tried to download the patch on it's own from the official site. Same error.

I had to uninstall the orig game (but saved all my saved games) and reinstall the orig then the EP....then added any hacks and such. But that was the same problem I had had.

Are you sure you've downloaded the patch? I mean, did the download complete? It's about 16.7 MB and it's specific to what install you have: CD or DVD. This is for the Original. There is no Uni patch out yet. Just install the patch by double-clicking on it.