I am not sure if you could do this on an iPad, but I can play video in the background on my iPhone 4S.
I do this by first open and play the video. I then click the home button, this of cause will stop the video, but you can then open the multi task bar, swipe to the right, click play on the video control. This should allow you to play the video in the background while you use other app. I believe you can also find apps that will play your video in the background automatically after you hide it. But if you want something like in the GS3 I guess we are out of luck for now.
I personally like how iOS handle multitasking as it is more efficient and I dont have to deal with closing apps as the OS deals with that for me. Still, I hope iOS will allow more options to interact with apps without opening them.
I just started on my Apple journey so I am not bored yet. I recently learned about shake to undo and speak selection. My iPhone now read out loud for me

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