To log errors in Free Snipping Tool, there are two ways. The First is via settings and the second is by placing an empty logerrors.txt file.
Why two methods?
Logging errors via settings will work just fine but it won't log application startup errors. If you are facing application startup errors you will have to use the file method. Otherwise via settings is enough to log most of the errors.
Enable Log Errors via Settings
Enable Log Errors via blank file
Note: Error logging can cause application lag so disable the settings and remove errorlog.txt after using it.