If you have two versions of that app on the phone, that could be your problem. It is really meant to only run one. If that is the case, try uninstalling one of the apps.
If that isn't what is going on, and you are having problems after say an update to the app, you can reset the app to what it was before any updates. Go into "Settings" then "Apps". Locate the app you want to alter and tap it. You should see an option to uninstall updates.
Also, it is completely possible that the ones you are trying to play have been restricted by youtube in some manner, which they do actually do with certain videos. So you may want to check if that is the issue as well.