Chromium on Ubuntu 14.04

The sites that don't work probably use the adobe flashplugin. Chromium needs a different flash plugin than Firefox uses to view flash media. My guess is that you don't have it installed. So,

Run the "Software and Updates" package, and on the "other software" tab, check "Canonical Partners". See the attached screenshot. Close, and reload the software lists.

Then install the package adobe-flashplugin.

If you had installed "flashplugin-installer", it will be removed, but that is ok since adobe-flashplugin will also supply the flashplugin for firefox.