On the dashboard, just have a search box that would keyword search in the activity entries. Like maybe someone had a conversation with a person, so they want to type that person’s name in the search, rather than searching for the case name, clicking activity sheet and scrolling to find the entry. So the search would have to return a page that would highlight the keyword searched and then you can click to go to that entry.
Proposed solution(client is ok with it):
Create a new view, expose a link to this new view.