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Permission wise you generally shouldn't have problems. Ownership in Linux/Unix uses numerical IDs, and on every major distribution the UIDs for regular users start at 1000, meaning the first user that is created during installation uses the 1000. Having a corresponding group with the same name is also pretty common. I'm pretty sure there are some exotic distributions out there which don't adhere to these practices, but I'd expect them to be rare.

> sometimes this breaks program in some mythical way, because a program in the new distro encounters some unexpected stuff left over by the old one

This really could pose problems. Quite often the version numbers of the same program will vary from distribution to distribution, so with applications, services and libraries which are used by a lot of distributions (dbus, GTK, QT, pulseaudio and basically every desktop environment, to name a few) will have a high chance of problems when versions differ, especially major versions where there are chances that the format of the configuration files changes, or configuration options are added which are unknown to older versions.

One solution I can think of is to place the "main directories" (Desktop, Documents, Videos, Pictures etc.) in a different place and just symlink them to the home directory for each distribution.