The ExtendedNotifications plugin allows you to filter notifications that are shown from the tray icon, and optionally log all notifications to a file. You can configure the plugin from Hacker > Plugins.
I find this plug-in extremely useful to monitor when the system does some stupid things by itself.
The problem is that the information logged is too sparse. Adding full path to executable/dll and command-line arguments would make it infinitely more useful especially for service hosts.
v2.34+ writes UTF-8 into the existing log file (which could be ANSI) and could cause the content to be encoding inconsistent.
I think you will not add an option for UTF-8/ANSI saving. But at least, it would be nice if BOM is added for UTF-8. Otherwise text editors could decode the log file using system default ANSI and Unicode characters will be garbled.