Hello,
Just to share the issue I have encountered with ESP8266 Thing and partially solved.
In order to reduce consumption, my ESP8266 Thing is always in deep mode sleep except when Arduino MEGA wake up it by pulsing DST low during 10 ms.
This works very well EXCEPT if I connect the Serial GP01/GP03 to the Serial of my Arduino. In this case, the ESP doesn’t start, maybe because the serial is already busy before the start and the ESP boot ROM programm can’t access to Serial to log its startup. Can someone confirm my assumption?
I found a workaround by using Serial.swap just after Serial.begin. This functions change the Serial pins of the ESP from GP01/GP03 to GP015/GP013.
Dear Sparkfun team, why GP015 is soldered to a resistor and not accessible on the Thing ? Luckyly, for my current project, I need only the RX pin GP013 which is mapped to your board 
, so I have connected the Arduino Serial TX to the pin GP013 and I have no more connection to GP01/GP03 and the ESP boot programm is happy !
Even if i have no more issue for now, I would be very interested to understand howSerial can block the ESP boot and it will be great to get GP015 mapped on your board like for the Thing Dev.
Thanks in advance