I think "ARP MAPPE" is Block Berthold Regular
http://new.myfonts.com/fonts/berthold/block-be/regular/

This is a really interesting question, which I hadn't thought about up to now. Later Schwitters used Paul Renner's Futura, but the Arpaden date from 1923, I think, so far too early for that. You could try mailing the Schwitters archive at the Sprengel Museum in Hannover (Dr Isabel Schulz is the contact) and asking there. Please keep me updated on this and I'll seee if I can't do a bit of research myself.
Regards,
Gwendolen Webster

Forgot to mention that the great-nephew of the founder of Molling is still alive. He's called Freddy Godshaw and lives in England.
Gwendolen

Thanks to you both. I agree that it's a font in the Block Berthold family too.

Can anyone confirm my questions about the type itself - whether or not these titles and subheadings would have been printed from wood (and not metal) type? And if so, does anyone know if those type bodies would have been end-cut, die-cut, or manufactured by some other method?

Is it any help at all that Molling used flatbed printing? Probably not.
By the way, there is a Merz picture entitled Merz Mosaic of Quartered Ornaments (now at the Sprengel), dating from 1924, a grid-based composition made up of letterpress blanks. Isabel Schulz suggest KS made this while working on Merz 7, and a variation of the picture is to be found in Merz 7 itself:
http://sdrc.lib.uiowa.edu/dada/merz/7/pages/70.htm
- it's difficult to imagine the blanks came from anywhere else than Molling.
It has also been suggested that Schwitters used lithographic stones from Molling to produce the Merz Mappe, or Merz Portfolio, of 1923. Sorry this doesn't answer your question, but its easy to get diverted with Schwitters...

To all who have participated, thank you! I am just returning to this topic, and to this thread, after a few years away from it and appreciate the responses.

A follow-up question: to those with an eye for these things who have suggested Block Berthold Regular -- do you think the Molling book Kling Klang (specifically the headings "4 TÖNENDE BILDERBÜCHER" and "KLING KLANG") is the same font?

http://blog.paperboxx.com/archives/2374

Yes, I do know this fantastic work. It is somewhat possible it was made at Vogt, though, since that is where they typset Die Scheuche. But Molling is very likely too given the date. Edel Sheridan-Quantz has done a great deal more research on Molling in the mean time. Do you know her work? She published an article in the KSUK newsletter about Schwitters and Molling.

Yes, it looks like the same font to me.
Ckick here for a comparison. Even the hyphen "-" is at the same height.

PS: Don't expect much more answers on this thread, because it belongs to the old, abandoned type-id section.
It's better to post a fresh question on the new type-id section and refer to the URL of this thread.