Steven Zahm@ Tim
RE: Weirdly it also changed some of the Single Entry page aesthetics.
Not weirdly :)
Because the Single Entry Template option was enabled, the active template for Individuals was the Default Entry Card and the active template for Organizations was Circled. With the options disable (the default) Circled is used for both entry types. The different templates have different layouts.
RE: I tried drag and dropping the content blocks into the desired order when Editing the Entry and it just reverts back to the previous block order when I publish the update.
Are you referring to the metaboxes on the Add and Edit entry Connections admin pages? The order of these do not affect the order of the fieldsets. That is controlled by the template design.
That said, if an entry has multiple addresses or phone numbers, you can drag and drop those within the metabox to change their order.
Now, if you mean the Content Blocks settings found on the Connections : Settings admin page under the Display tab. Changing their order does affect their display order in the template and should save. Reviewing your site, I do not think this applies to what you are asking.
I hope this helps!