I've found the most reliable way to install flashplayer is to retrieve it from the partner repository.
Use your package manager to activate the "partner" repository, or simply remove the hash mark from the beginning of the line:
in /etc/apt/sources.list. Then update the repositories and install adobe-flashplugin. From the command line you can simply do:
deb http://archive.canonical.com/ubuntu precise partner
I've never had any problem watching videos at YouTube (or anywhere else) when I use this method.
sudo apt-get update
sudo apt-get install adobe-flashplugin