When clicking on the number of actions from the Notes and Actions tile in a constituent's record and getting a list of that constituent's actions, any filters set there should be persistent or have the option of being made persistent/saved.  This can be done in an Action List but does not appear to be able to be done when accessed via a constituent's Notes and Actions tile.  The reason for this is that the fundraisers using this feature won't always want to see all the minor things, globally added things, and so forth, and would like to be able to filter in quickly to the important actions such as meetings and phone calls (what the web view itself calls High Value actions, although the users want their own filter options, not just an option for the BB-defined High Value actions).  While Filters can be set on this screen, it appears that as soon as you leave it those filters are lost and have to be re-set every time.