Bluetooth Serial example un Puck

Not really - Bluetooth data will get reliably to the Bluetooth stack, but if it's not handled by Espruino fast enough it'll get lost (however a FIFO_FULL error flag gets set in that case).

Can one handle this error within the application code? I've tried overflowing by sending loads of data in a loop, but it seems be be fine. At least that is encouraging!

Having said all that the datarate over BLE is pretty low with the standard MTU and there's a big input buffer, so it's entirely possible that you could write your code such that it can always handle data as fast as can come over BLE.

Yes, it looks like it works for now. That's something we can work with at least.