Are you using the web page or an app? Some web pages include code that mobile browsers can't handle. I tried Safari, Atomic, and Puffin. None of them worked with the standard web page. There might be others that do, but those are the only three I have handy.
You can work around this by going to the m.facebook.com pages instead. These are optimized for mobile browsing. Unfortunately they also assume you're on a phone, so the UI is very basic. But you can add notes this way. It is just sort of ugly and the editing capabilities are limited.
I use the app Friendly. You can do most things in FaceBook with it, including notes. The UI is nice and the app is cheap; either free, or 99 cents if you want to nix the adds.