How can I get an old version of the YouTube application for Samsung Galaxy Tab 2? The new update is slow and poor display.
If the YouTube app came with the phone (ie is a system app), you can uninstall all updates to it. Go to the application settings page for YouTube to find the button to uninstall updates. This will roll back the app to the version that existed when the phone/rom was brand new.
On the other hand, if it isn't a system app, you'll have to go online to find an old version. And you will have to first uninstall the current version, which will remove any preferences or settings you have set.
There is no way in the current Play Store to choose the version of an app you want. The Play Store decides what version you get (usually the most recent, or the most recent available for your device/OS), and you decide if you want to install the update or not.