I am having same problem on my Lumia 830 (non-Insider 14393.448).
Few weeks back I had hard reset my phone, after that 2 problems started, earlier both these problems were not present. After factory reset I did not restored backup data. So phone could be considered completely fresh. Even I had format external memory card after Phone was reset.
First problem is about All Contacts Picture lost and Gmail contacts are not syncing (mentioned this in some other thread).
About Calendar Live Tile, I have observed that Tile is not updating, and it continues to show previous date or no date at all. This happens in all Tile size - Small, Medium and Large Wide.
Workaround is to resize Tile size and it will display updated information.
Calendar date and events are displayed correctly on Lock screen.
Outlook Mail and Calendar are updated several times after I did hard reset since 2-3 weeks back, but this issue is not getting resolved.