Share your experience!
I use Polar Flow app to synchronize my training sessions from Polar V800 to the web:
Polar V800 - bluetooth 4.0 - mobile - https - flow.polar.com
I have upgraded from Z3 compact to Z5 compact. Nothing else changed.
Since then the synchronization is almost impossible. The syncing process fails after 30-60 seconds every time. If I am lucky the current training session can be uploaded to the mobile after 5-10 attempts.
Bluetooth HCI snoop log was fine on Z3 compact but not on Z5 compact. Wireshark detected some inconsistencies in the Z5C's bluetooth log: it has been cut short in the middle of a packet.
So I think the bluetooth connection drops very often during data transfer.
I'm sorry to hear that 
You may experience stability issues when connecting your Xperia Z5 Compact or your Xperia X to a Polar V800 GPS sports watch. The issue is due to a bug in the bluetooth chip. It will be fixed in the next software release.
Note that software rollouts are a phased process - timings & availability may vary by market/carrier.
Fingers crossed (waiting for the solution since my first post in last November)
Thanks for the info, Rickard!
Just to be clear: you are suggesting that the next FW release after the current 32.2.A.0.253 will contain thix bluetooth chip bugfix?
Thx!
Unfortunately, this bug is present in the new firmware 32.2.A.0.253 
So, after 11+ months of waiting the current firmware (.305) finally works well with Polar V800.
Yesterday and today synced daily activities and 2 training sessions with success: bluetooth connection was stable.
I hope that the next firmwares (Android N) will not ruin this.
Summary:
32.2.A.0.305 - OK (2016 Oct)