Arc2Earth Debug Log
Arc2Earth Desktop creates a log file used to help diagnose any crashes, bugs or problems with the software. The file is recreated every time you restart ArcMap so if you have a crash, make sure to copy the file prior to restarting
From Arc2Earth UI
Arc2Earth Toolbar -> Help -> Options -> Show Debug Log

You can also get your Arc2Earth Support info by clicking "Copy Support Info" button. This very helpful for technical support issues.
From Windows Explorer Windows XP
C:\Documents and Settings\{{user_name}}\Local Settings\Application Data\Arc2Earth\DebugLog.log
Vista and Windows 7:
C:\Users\{{user_name}}\AppData\Local\Arc2Earth\DebugLog.log