Permanent way to keep youtube playing in iOS5
You could use a different app for playing Youtube videos, which don't stop playing when you press the home button. YStream/Ystream2 is an example of such an application (amongst others).

As far as I know there is no way to prevent the built in Youtube app from stopping playback when the app is "minimized". These are the ways I know of for resuming playback:


Double tap the Home button, slide the bottom row, and press play. (As you mentioned)
Lock the screen, Double tap Home button, Press Play. (I usually find this slightly faster)
Use a Bluetooth keybord with a "Play" button.
Activating VoiceOver and double tapping the screen with two fingers.
Using the Play button on your headphones.