I haven't been putting plastic items in the dishwasher at all after reading about BPA leaching into food after plastic is damaged by the heat it is exposed to in the dishwasher. Apparently you can't necessarily see the degradation that washing plastic items in the dishwasher causes. This article is about why weight loss may be stalled, but Number 2 explains about why washing plastic in the dishwasher is a bad idea. This isn't the only place I've read it. About light things flipping, the only suggestion I have is making sure the light item is wedged pretty tightly between other items. That doesn't work all the time though.

Here is a link that might be useful: Plastic in the dishwasher

I have this problem with a few things. There are wire baskets sold to contain the small pieces for baby bottles. Most are expensive for what you are getting and may not be the size you need. I'm still searching.

Google the words dishwasher basket to see what's available. Here is the best I have seen:

Here is a link that might be useful: Dishwasher basket

I have that problem too, that & none of it gets dry in the dishwasher. I sometimes run a second dry cycle. Or I have to dry or let item sit on counter to dry.

Just weigh down the light items with clean plates or bowls. Four pasta bowls space out perfectly to anchor all the light items in the upper rack in my dishwasher. No more problems with flipping containers.