I wish I had enough water storage for it to sit longer than a week, but most of my reservoirs turn over every 48-72 hours. Some individual tank reservoirs do hold the 7 days between changes. Other than the diatom films (which I also consider a plus) - all silicates and other minerals used in the reservoir are that much less to go into the tanks.
Storage bins, reservoirs, water butts, etc. should be suitable for potable water storage. Beyond that, only structural strength and avoiding damage by localized heating, as Harlock already mentioned, really matter. A bit of aeration is a plus but not essential.
Ashdavid - Dr. Adey used and popularized algae beds, but he was not the originator. That predates him substantially.