iPhone cannot play every Youtube content. Probably, your iPhone will show following message:
This video does not currently support iPhone.
Even you can check with the following video with your iPhone. It can be played on any computer, but not on iPhone.
Is some Youtube video format different? Or, do some videos have copyright? Maybe is it because it doesn't show any ad while playing?
Recently, Youtube got another option not to show some videos on mobile devices and TVs. If you can edit video, you can find out the syndication option. In this option, you can specify your video to show on movile devices or TVs or not.