Not entirely sure I understand what's going on, but would appreciate some pointers or things to try.
In an incognito window, try loading http://ireland.media.info - and look at the search box on the right-hand side. It's falling off the bottom of the top menu bar, isn't it? Looks really ugly, doesn't it?
Now, hit reload. Look at the search box on the right-hand side. Oh. It's displaying nicely in the middle of the top menu bar, isn't it?
I've been writing HTML for twenty years, but never seen this.
Is it, perhaps, a bug related to the images on the left, which are browser re-sized (so they look pretty on a retina screen)? Is it a bug at all? Are you seeing this issue on any other browser or any other build of Chrome for another OS?
(Just so you know: the HTML should be identical for each load, and, indeed, should be cached at the server using Varnish anyway.)