Https sites not displaying correctly

Question

Here's an interesting problem thats cropped up on a couple of machines here. Hopefully someone else has found the cause!
The problem is that some HTTPS sites are not displaying correctly. We have seen this with vimeo, and with wetransfer. I have included a screenshot of the issue on both safari and on chrome.
Cross checks i've been able to verify:
another machine with the same OS (10.8.5) looking at the same sites is fine and another running 10.9.4 is not, so this appears not to be OS or browser version related.
this does not happen in a different user account on the same machine, so the issue appears to be in the user home.
this happens across all browsers in this user account. so it appears to be a supporting technology or cache going wrong rather than a specific browser.
I have emptied the user preferences, and cache folders with no change.
Clearly i can sidestep this by creating a new user home, but that isn't actually getting to the bottom of what is going wrong, and it would be better to identify the issue!

Answer 1

Please read this whole message before doing anything.
This procedure is a diagnostic test. It’s unlikely to solve your problem. Don’t be disappointed when you find that nothing has changed after you complete it.
The purpose of the test is to determine whether the problem is caused by third-party software that loads automatically at startup or login, by a peripheral device, by a font conflict, or by corruption of the file system or of certain system caches.
Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards, if applicable. Start up in safe mode and log in to the account with the problem. You must hold down the shift key twice: once when you turn on the computer, and again when you log in.
Note: If FileVault is enabled, or if a firmware password is set, or if the startup volume is a software RAID, you can’t do this. Ask for further instructions.
Safe mode is much slower to start up and run than normal, with limited graphics performance, and some things won’t work at all, including sound output and Wi-Fi on certain models. The next normal startup may also be somewhat slow.
The login screen appears even if you usually login automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.
Test while in safe mode. Same problem?
After testing, restart as usual (not in safe mode) and verify that you still have the problem. Post the results of the test.