What was presumably happening was that the 'background agent' part of Photos was crashing silently and then unable to update the live tile - in any case, the update yesterday has fixed the issue on all my test phones and images are happily rotating (as in content, not err..... orientation!) as they used to. Phew.
Here are appropriate 'before' and 'after' screen grabs - from placeholder to glorious sunset!
You can grab the update yourself by checking 'Downloads and updates' in the Store - if you haven't already. And keep an eye on that live tile - it should work just fine now.
If this sounds like a minor bug fix then it probably is in the grand scheme of things. But the Start screen and its presentation of info and favourite things is one of THE unique selling points of Windows Phone and Windows 10 Mobile - so to have this broken was a crying shame. Especially with Photos set to the 'large' tile size as shown above.
PS. I keep the live tile set to 'Favourites', by the way - though you can also switch it in Photos/Settings to 'Single photo' or just 'Recent photos'.