This is an annoyance, but not a huge problem.
Group Moderator actions:
1. Click Admin > Activity to display the Activity Log.
2. Type something into the Search box and click the Search button.
3. Now clear the Search box, and click the Search button again, which should restore the full un-filtered Activity Log.
4. Surprise -> the previous contents of the Search box re-appear! And I'm seeing the filtered Activity Log.
5. The same thing happens if anything is selected from the list of Activity Actions. The Search box always reverts to what was there previously. Except ...
6. Except if my search string had an asterisk, which gets replaced by %2A when it reverts to the old text. Now it is actually searching for "2A" and ignores the "%". (I guess "%" is not an allowed search character?)
The work-around is to start over: click "Activity" in the left menu again. So it is an annoyance but not a show-stopper.