Hi tcat007,
I think that plywood can be an OK “stopgap” solution for the short term but it also has some disadvantages and I don’t think it’s the best long term solution for supporting a mattress.
If you put plywood on a flexing boxspring it won’t be as stable and will have more sway (and possibly noise) than putting a mattress on a more rigid foundation.
It will also restrict airflow under the mattress which in combination with other risk factors can increase the likelihood of mold and mildew and even the dust mite population (they like warm, humid environments with little airflow) . There is more about this in post #10 here.
If you do choose to go in this direction I would make sure that the plywood was finished on at least one side to reduce the risk of splinters and snagging and damaging the mattress cover (and possibly reduce moisture as well).
Plywood also uses glue with solvents so this may be an issue for some people.
Finally, while I personally wouldn’t go in this direction unless there were no other good options or I was only thinking about short term use, for those who do I would use 3/4" plywood to prevent the risk of sagging under the heavier parts of the body over time.
Phoenix