Thanks for the links. I focussed on the demo post for now, since the responsiveness isn't designed to work with embedded PDFs so the Luxembourg gallery is a better one to test with. I had a look at it on iPhone (iOS 6 & 7) and iPad (iOS 7), both in Safari. I also used the Resizer bookmarklet to test other screen sizes.
So far I haven't been able to see any layout issues on this end. The header image fills the width of the screen as expected, and the tiled gallery looks fine. There is a bit of white space on either side of the gallery, but that looks normal to my eye and unlike the "messy" display you refer to. Here are some screenshots from iPhone/iOS 7.0.3:
I wonder if you'd mind uploading a couple of screenshots to help in troubleshooting?
Here's a guide on how to make a screenshot, if you're not sure: http://en.support.wordpress.com/make-a-screenshot/
You can upload the screenshot - in a graphic format like JPG, PNG, or PDF - in your Media Library, and provide a link so I can see it, or upload it with a service like Droplr or Imgur.
For each screenshot, could you please let me know the OS, device, and browser you're running? Thanks a bunch.