My dishwasher has been doing this for some time now. Most of the plastic dishes (plates, tupperware, small bowls) have a white powdery film on them after the dishwasher runs. I can run my finger over it and some of it will wipe off, but it also kind of smudges when I wipe it. This doesn't happen to glass and ceramics, just plastics. I use pods and a rinse aid. Any ideas as to what may be causing this?

When ours does this I run a bottle of dishwasher magic thru and it cleans it out for a few months. Not sure what actually causes it.

Have you cleaned the filter recently?

I clean the filter and run the washer empty with a cup of vinegar about once per month. We are a family of 5 and we run the dishwasher pretty much every single day. I have changed rinse aid, tried no rinse aid, etc. and still getting the issue. Dishwasher is probably 5 years old.

Water hardness?

1. IF this is hard water, THEN a solution might be
Cascade Platinum Plus ActionPacs Dishwasher Detergent Pods
which claim to NOT need a rinse aid, since this is built-in
https://www.hydroflow-usa.com/texas-water-hardness/

2. IF this doesn't solve the problem as advertised THEN the pods may
not be a good marriage with this machine & its water, so try the
Cascade powder, THEN the liquid

3. We never have this problem for decades, no matter the DW brand & always use Cascade Liquid ... Aggieland 8 PPM (mg/L) or 0-5 gpg (soft)

Please educate us when a solution is found?

We had this problem, then switched to Cascade Platinum pods and the problem went away.

Oddly enough. We switched to the finish pods from
Cascade and it fixed our problems. We also run a vinegar cycle about every 6 months.

Tried switching to pods and had this same problem. Went back to liquid and it's fine.

Here's the details:
College Station water, Cascade dishwasher pods (sometimes platinum sometimes complete), usually cascade rinse aid (sometimes cheapo store brand - but hasn't changed the issue when this is changed), periodic cleaning of filter and vinegar cycle

I'll try changing detergent brands then style (powder or gel) and report back. Thanks for the ideas!

your new details
bring one more idea to mind, regardless of what the DW manufacturers say about hot water they manage ...

Wellborn Water
Cascade liquid
Any brand Rinse
then
Running the neighboring sink water until it's HOT
then
running the DW

The hot water ready to go has even solved some pods-making-powder problems around here but not always.