Even though it is still summer, I am frequently contacted by students seeking advice. A common production situation is shooting in someone's borrowed apartment... echo prevails, but the landlord prohibits modifications.
There are some simple and inexpensive remedies.
Many of the discount department stores (Target, Walmart, etc.) sell egg crate style foam pads for mattresses. These pads are large enough to cover full or queen sized mattresses, so they are pretty big. I have seen these pads as thick as 2 inches. So for just a little bit of pocket change, you can purchase a great deal of acoustic wall covering! This padding also makes for great window or glass door covering; not only does it block echo and reduce outside noise, but it also serves to block incoming light.
Another solution (my favorite) is to create wall panels that will become part of the set. You can find 4x8 sheets of "sound deadening board" at any bona fide lumbar yard. Don't bother looking in Lowe's or Home Depot; go to a real lumbar yard that contractors frequent. Sound deadening board looks like compressed cardboard.(see illustration) It is moderately lightweight (compared to wood, especially compared to compressed wood particle board) and not very expensive at all.
Cover these panels with inexpensive cloth, such as linen or burlap. Easy task, only requires a scissors and a staple gun. Purchase the cloth in bulk (bolts) from a fabric distributor.
To install the panels in the apartment, just remove whatever framed artwork or wall hangings are already there, and lean the panels in place up against the apartment walls. If the wall hangings are not copyright protected, you can re-hang them onto the deadening panels.
Your Art Director or Production Designer may opt to use these panels as an excuse for getting creative. The cloth covering does not have to be plain white; they could opt for a color or pattern. The cloth could also be dyed or even painted.The panels could be cut down to slimmer widths, and hung various ways for visual effect. For example, diagonal or horizontal slants can create a very avante garde appearance.
The panels do not need to cover every inch of apartment wall. Even sporadic coverage will improve the acoustics immensely! The panels will reduce outside noise and eliminate a ton of echo. Unlike furniture pads and mattress foam, these panels become part of the set and do not have to be jockeyed around to accommodate lighting & camera.