Hey all, I'm not sure if this is related to the same problem you're encountering, but I thought I'd re-post this here in case it helps anyone.
I opened up Pages & Numbers on my iPad this evening, and all the icons were black. Clicking on any of them gave me the 'Document can't be opened' message. If I signed into iCloud.com, I couldn't download the documents either.
After a lot of messing around, it seems like it was something to do with file conflicts. Maybe this all happened when I updated to iOS 5.1 or the new Pages/Numbers App updates last week? I don't know, but somewhere along the line, the file conflicts were blocking all documents from being accessed and synced properly.
The way I fixed it was to fire up Pages & Numbers on my iPhone. It showed me my documents, but when I clicked on them, they told me there were conflicts in the files, and presented me with two options, one a black icon, the other a normal document icon. I clicked on the normal one, and the document seemed to open and load. Additionally, with Numbers at least, the files all updated on the iPad too, and all the documents could now be downloaded via iCloud.com. I had an issue with Pages on the iPad, in that it wasn't updating the documents as I was fixing them on the iPhone, so I simply uninstalled Pages on the iPad, and then re-installed. Once iCloud was enabled, all the documents loaded up properly.
I really can't say if this is the same issue you're experiencing, but I figured I'd mention it.. just in case!!
Also, another tip.. until iCloud gets fixed-up good 'n proper, for your own piece of mind, whenever you edit a document in Pages/Numbers/Keynote, just before you finish-up, hit the 'wrench' icon, choose the 'Share and Print' option, and then click 'Save to iTunes'. Choose the first file type, and it'll save a copy in a different location on your iPad. It only adds a few seconds to your workflow, but could save you a LOT of heartache. If a file gets corrupted by Pages or deleted/corrupted by iCloud, you can simply click the + button on the Documents page, and select 'Copy from iTunes'. This will show you all the documents you saved. They'll also show up in iTunes should you want to pull them off the iPad quickly.
Good luck!