I've heard of the coolant temp sensor leaking, but has anyone ever had a leak in the thermostat? I'm attaching a picture. I'm about to purchase a new thermostat and I'm wondering if this is a known issue. The check engine light came on and the error code pointed to this sensor.

 

I'd be careful of allowing OBD readers to interpret codes. Most codes are proprietary and therefore come out just a little incorrect. I highly doubt that your reader is accurate on this one because a leak is a physical issue not a logical one. No way a computer is going to know that there is a problem with an o-ring and which one. Just does not work that way.
I personally have never heard of the above but anything with an o-ring can be susceptible to leaking. Have you physically inspected the car? If there is a leak there should be something visible. There is a coolant temp sensor that is prone to leaking. It's a cheap part $25 or so. I changed mine out a few months back after I noticed it leaking.

 

Yes, I physically inspected the car.

The OBD2 reader did not say that there was a leak, but that there is an issue with that specific sensor/connector. After unplugging the connector going into the thermostat I noticed the leak.

 

Okay, just updating the thread for anyone who gets the same error code (P0598.) After replacing the thermostat and re-setting the ECU, the error disappeared. Usually it would come right back on, but this time it stayed off.