stops between Mittenwald and Berlin?

Rothenburg ob der Tauber is not directly on the way. When going there, you will probably go through Nuremberg, which is a worthwhile destination itself (another route takes you through Augsburg, which is also worth a visit). Bamberg and Erfurt are other destinations between Munich and Berlin which are worth visiting. Personally, I'd skip Rothenburg and choose any one or two of the other towns I have mentioned.
I assume that you will visit Munich separately? If not, that would be the most obvious candidate...

How much are you willing deviate from the train route? If you're going by car, then obviously you will enjoy more flexibility in choosing an interesting place somewhere in between.

By train then I suggest these different places...Weimar, Jena, Leipzig, Meißen, Ingolstadt, Erfurt, and especially, Naumburg if you want to see German cultural history.

Thanks for your help, everyone. We decided to go to Rothenburg-ob-der-Tauber, and we want to travel from there to Berlin by train on a Saturday. We were advised to get advance reservations.

We’re finding a bit confusing to book tickets on the Bahn web site. Once we are in Germany, can go to a station and we buy ticket for a future date?

We are two older people traveling with medium-size suitcases (not carry-on size). Is it reasonable to select a route in which the transfer time between trains is only 4 or 5 minutes?

What happens if we buy a ticket and can’t make the transfer in time? Is it better to just get reservations for the Berlin leg of the trip and make the trip from Rothenburg-Nurnberg without reservations? We could allow extra time in case we miss a connection.

Thanks again.
Susan

We’re finding a bit confusing to book tickets on the Bahn web site. Once we are in Germany, can go to a station and we buy ticket for a future date?

It's better to book in advance since you can save up to 50%. Please tell us what problem you are having with the DB website; it shouldn't be difficult to cope with it.

We are two older people traveling with medium-size suitcases (not carry-on size). Is it reasonable to select a route in which the transfer time between trains is only 4 or 5 minutes?

That depends on the station and distance to cover between the two trains. For your trip from Berlin to Rothenburg, a four minutes transfer time in Steinach is standard and easily doable; same holds for Ansbach (where you transfer to the train for Steinach). I'd be a bit reluctant, however, to select a four minutes transfer in Nürnberg if it isn't a same or adjacent platform transfer. I'd allow 10 min minimum.

What happens if we buy a ticket and can’t make the transfer in time? Is it better to just get reservations for the Berlin leg of the trip and make the trip from Rothenburg-Nurnberg without reservations? We could allow extra time in case we miss a connection.

If your train is late, you simply take the next one. Rothenburg to Nürnberg is usually local traffic - no reservation possible. BTW, if you buy a reservation it's valid for all trains in sequence for which a reservation is possible. You don't have to buy an extra one for each train.

Thanks. It's getting less confusing. Someone told me the difference between national trains (ICE, IV, EC train) and regional trains (RE, RB, IRE train), so that helps, too. Can we buy a ticket from Rothenburg to Berlin and just take any train, with the exception of the train to Berlin?

RS recommends staying at least one night to avoid the mass crowds of day trippers who arrive by tour buses but leave mostly before dinner. The town is nice when not overrun by tourists, and the church windows and altarpiece are brilliant. I don't think 2 nights are necessary if you get there early in the afternoon and leave in the middle of the next day.

Nuremberg is the jumping off point from the Munich to Berlin main line for a side trip to R-o-d-T. It is a great place to visit too.

https://museums.nuernberg.de/nuremberg-municipal-museums/

Have fun.

Can we buy a ticket from Rothenburg to Berlin and just take any train, with the exception of the train to Berlin?

The best connections are via Nuremberg. There are only regional trains between Rothenburg and Nuremberg (apart from an occasional IC from Ansbach to Nuremberg). You can take any of those, even if you have bought a train-specific saver fare ticket for the ICE ticket from Nuremberg to Berlin. ++)

BTW, there would also be a connection with regional trains via Würzburg to Bamberg, but it takes longer and there are less ICE connections from Bamberg is lower since not every ICE stops at Bamberg.

++) The connection specification on your ticket would read something like this:

Rothenburg - Berlin mit ICE
Über: NV* Nbg-Hbf ICE 506

"NV*" means "any local train" - there is no specific train number. "ICE 506" on the other hand means that you have to take exactly this train in Nürnberg ("Nbg-Hbf").