Field Formats magically displaying different formats than preset (date, time)

Field Formats magically displaying different formats than preset (date, time)

This is a curious but - for us - crippling issue, and it has surfaced completely out of the blue. 

Throughout various Modules we use date and / or time fields for related data. For example, date of birth, date of appointment and so forth. 

This morning, the date of birth field suddenly no longer showed any data for any record of any Module.

On examination it became clear the data was there, but no longer being displayed - it looked as if the field was suddenly empty. When selecting the field, data did become visible, but not in any way matching the preset date format. Instead, a field limited to date didn't just show an incorrect format, it also displayed time in an odd format. 

During a support session it was considered that it might be a browser issue. Unfortunately, clearing cache & cookies & all that as outlined by support made no difference. 

By this afternoon, every field using data and / or time is showing the very same problem. 

But it gets even more weird. Testing this problem on different PC's the problem isn't consistent across pc's. On one laptop a field will show as blank, on another it will show data in an incorrect format. The very same field on another laptop will say "undefined". 

Thoughts? Suggestions?