To be absolutely honest, I don't believe it is a Joomla! issue. This issue has not happened on any of my Joomla! 3.5 sites (3.5.0 and 3.5.1) during development and testing. With the intensity of the testing I performed I have visited that page at least 300 times every day for three weeks. If there was a problem I'd have most assuredly noticed.
On top of that, the way this page is rendered has not changed since December 2009 when I first wrote it: the server generates a JSON string, it outputs it to the page body and then a script file reads it and renders the configuration interface fields. Since you're from the USA I assume that you're using Akeeba Backup in English so there's no chance that some exotic character is screwing up the JSON. That does leave us with either a Javascript error or a stale browser cache. Which brings us to the next point.
Akeeba Backup 5.0.2 was released 9 hours ago and is of course fit for use on production. This is what we are running on our own site (and yes, the configuration page does work!). Please remember to also clear your browser's cache. This is important, since the browser may be serving the cached interface script file from an older version of Akeeba Backup which is NOT compatible with Akeeba Backup 5.
Nicholas K. Dionysopoulos
Lead Developer and Director
π¬π·Greek: native π¬π§English: excellent π«π·French: basic β’ π My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!