You can, but it's not obvious.
Start with a blank new text file open in Notepad or whatever, and open the eraser schedule. Right-click on the task to view the log in the usual way. Click on the first entry in the task, then press Ctrl+Shift+End to select the whole log text. Right click on your selection, and you get an option to copy it into the clipboard. You can then paste your selection into the text file.
Note that you may have to copy and paste the last line in the log separately. I think this is a bug; Joel doesn't.
David