How do I view the list of podcast chapters on an iPad using iOS 5?
There really doesn't seem to be a way to view this info at all on iOS 5 iPads, in Apple's "Music" app. 

Further iPad iOS 5 podcast annoyances:


If the main "Music" you listen to is podcasts, it's really annoying that you can no longer promote the "Podcasts" button from "More" to the main view: so you always have to go to "More" to see your podcasts.
If you have a mixture of video and audio podcasts, you have to switch between the "Videos" and "Music" apps to see them.


For all these reasons, I gave up on the built-in iOS 5 podcast tools, and switched to Podcaster. It costs a small amount of money, but has so many convenience features built in that it's well worth it.

(It's actually iPhone only - but works fine on iPad, at 2x size, even for showing videos)

I particularly like:


It downloads the latest episode of shows you subscribe to, but seamlessly shows you earlier ones too, so you can easily stream them
Automatic downloading via WiFi - so no more need to connect my device to a PC to update lots of podcasts
Back and forward buttons to go move 30 seconds back or forwards - or you can change the settings, and make these buttons go back/forward 10, then 20 then 30 seconds if clicked in quick succession.
Small icon at top-right of screen shows/hide details of podcasts.
Sleep facility (15, 30, 45, 60, 90 minutes)


(I'd like to include a link to the original question here where I saw Podcaster first mentioned, but there are so many answers singing its praises, I really don't remember which one I saw.)

Edit

And to answer your question about Tiesto's Club Life Podcast, yes, Podcaster displays that well. It shows the images as you listen, and at bottom-right of the screen there's a little chapters icon that shows name of each chapter, and its position (in minutes and seconds)

Furthermore, you can swipe upwards on the screen, when playing, to show the chapters.