Unfortunately, there is almost no log, neither in TTN Console, nor when subscribing to the MQTT error events topic.
If the MIC fails, then TTN won’t know which device the failure belongs to, as it needs the MIC to find the device. So then it simply cannot log anything. For replay attacks (which, in terms of security, really is what re-using a lower frame counter is about) TTN does know which device it’s rejecting the frame counter for, but unfortunately does not log that either.
The only errors I know that are logged are OTAA shows "Activation DevNonce not valid: already used", Activation not valid - no gateways available, and errors during execution of payload formats (only published to the MQTT error events, not in TTN Console).
Sure, for testing it might help. It might even help for debugging, though like mentioned in the warnings I already linked to above, just changing any setting of an ABP device will also reset the downlink counter, which for a production device can be really troublesome. In this very case, the uplink counter in the first screenshot was at 7941, which does not seem to indicate the device was recently reset.