It's almost a perfect drop-in replacement for Docker so I don't see why it would be any less "set-and-forget".
I only ever found one thing that didn't work with it at all - I think it was Gitlab's test docker images because they set up some VMs with Vagrant or something. Pretty niche anyway.
The one edge case I know of (and have run into) is that podman push doesn't support the --all-tags flag. They have also said they do not plan to implement it. It's annoying because that flag is useful for CI scripts (we give multiple tags to the same build), but not the end of the world either.
I could not get LocalStack to work on Podman, to my chagrin.
And no, doing the "sudo touch /etc/containers/nodocker" thing didn't solve it.
In fact, there is even a package "podman-docker" that will alias podman to docker so most of your commands will usually work without modification. (of course, there are always the edge cases)