ORA-00922 encountered in Oracle 11gR2 installer
I found a solution on my own! 

It seems that there is a bug in the Oracle installer - it doesn't like it if you start your system password with a number. 

I completely uninstalled Oracle using the deinstall utility and then reinstalled Oracle, this time specifying a system password beginning with a letter. This solved the problem! 

I hope this helps anyone else encountering this annoying issue.

Additionally, user HanFromBs found that the installer doesn't like special characters (- or +) at the start or end of the password, so watch out for this too.