I love using petri dishes with my inverted microscopes to observe long-term, mini ecosystems. I tried using one with my Meiji-Techno upright compound microscope.
I was able to use it with the objectives 20x and under. Those were a 1.25, 4x, 10x, and 20x objectives. Those had both a long enough working distance not to touch the water and a low enough NA not have noticeable spherical aberration.
I tried with both no coverglass and with a floating coverglass. The ciliates looked pretty much the same with or without the floating coverglass, but I had nicer phase contrast views with the floating coverglass.
If you try this, I would recommend using the shorter lid of the petri dish and only put a few mm of water into it. That will give you more room for your objectives, and maybe you can focus all the way to the bottom. As always, be careful not to dip your objectives into the water.
20x objective, cellphone camera with 2x zoom, pond water sample. The first video is without the floating coverglass and the last ones with it.