Making a rest invisible changes its position to "automatic clashing"?
With 2 parts on a staff in staggered 16ths with rests correctly positioned, select a 16th rest and make it invisible, and it suddenly leaps up into the other voice and sits there clashing. This is a bit annoying especially because MuseScore draws invisible elements on top of printed elements, so you get to see your score become a mess unless you take the time to drag the newly invisible rest back out of the way into its correct position. And then if said rest needs to be made visible again, its position then jumps to a brand new wrong location, and has to be dragged again. All this obviously has to do with "automatic placement". Searching the forum it seems the current behaviour may have been done intentionally at some point before auto-placement in response to users asking for invisible rests to not take up space in the layout? The solution seems to have been to automatically move invisible rests into clashing positions? Anyway it doesn't quite make sense to do that since moving the rest back out of the way once it's invisible doesn't change the layout, it's now unnecessary to make the rest leap into a clashing position in order to save space, so I think the behaviour should be changed.
You can set up a shortcut ( [Edit]>[Preferences]>[Shortcuts] ) to toggle show/don't show invisible items. Of course, the downside of not showing invisible items is that you can't see them to select them.
In reply to You can set up a shortcut ( … by SteveBlower
You can however, select the invisible rests through ordinary keyboard navigation. And the same for any other notes or rests that appear obscured by the grayed out rests on screen. Plus there is Ctrl+click to select elements underneath other elements.
Personally, I'd never bother moving one of these rests, I'd leave it alone then possibly turn off invisible elements if for whatever reason I wanted to see what it was going to look like printed.
You are correct about the why of the current results of making a rest invisible. They were causing extra space between staves that wasn't necessary.
I never drag rests, I use the inspector to move them where I want them. I select the rest click the Y offset and spin my mouse wheel and the rest moves up and down. To put anything back where MuseScore originally had it, select it and press ctrl+R. You can shift+click any note it overlaps and both will be selected and you can press ctrl+R and only the rest should move if the notes wasn't adjusted.