Munich to Vienna to Krakow to Salzburg then back to Munich via rented vehicle

All of these countries (Germany, Austria, Poland; plus some combination of the Czech Republic, Slovakia, and/or Hungary that you will presumably drive through) are part of the Schengen area, so there are no routine border checks or stops at the border.

That said, the main things to watch out for when crossing borders in rental cars is:

• Expensive drop-off fees when returning your car in a different country than where you picked it up -- not relevant in this case if you're picking up and dropping off in Munich

• Ensuring you are permitted to take the car into different countries. When you make your car reservations you need to read the terms and conditions carefully to make sure you can drive the car into all the countries you have planned on your itinerary. Very broadly speaking, cars that are rented in Western Europe sometimes aren't allowed to be taken into Eastern Europe, but this varies a lot based on exactly where and what you rent.

Thank you, Andrew!

One other issue is to have the appropriate "toll pass" ( by whatever name) for each country you visit.

That may be the one 'border crossing' task you will need to attend to, as you travel from country to country

Ah, good to know too!

You for sure will need to get a vignette windshield sticker for Austria. And most major rental car companies will charge a surcharge for the car to go into the Czech Republic, and they won't let you take one of their premium cars into the country. It's a little over 500 miles (9 hrs.) and there are toll roads.
I used to travel such distances in Europe, but have since seen the light and now we travel "slowly."
You can also fly Munich to Krakow from $152. EasyJet flies it in 1 hr. 20 minutes.

Yes, we'll get the vignette...and are prepared for the toll roads.
And although the flight is short and cheap, we'd miss out on Vienna and Salzburg. We're planning a night, or two in both places.
Thank you for the other info though.