Copyright is based on authorship. So, while the main text of Mein Kampf is in the public domain, this new two-volume work will legitimately claim a new copyright. The new copyright will come from all those notes, which were created through acts of authorship. Contrary to the other contemporary story of Otto Frank, editorship is sweat of the brow, while authorship is creativity (see https://www.gutenberg.org/wiki... , for example). Translation does qualify as authorship, since is an intellectual creative act. (Dunno about machine translation...)
In the US, public domain items often have a copyright claim due to a new preface, or introduction or even cover art. Check some of the "Penguin Classics" in your local bookstore for examples. For Mein Kampf, all that added content will create a mixed item, where extracting just the public domain content (minus notes and whatever else is new) will take some effort. Luckily, the public domain text is already widely available without the new notes.
As mentioned, copyright expiry based on life+70 has no bearing in the US for items published prior to 1978 (https://www.gutenberg.org/wiki/Gutenberg:Copyright_How-To). Due to GATT, no copyright renewal was required after 28 years for items published outside of the US to get the full copyright term. The translations into English were not made until after the original German, of course. In the US, copyright will expire 95 years after publication based on the current USC Title 17 (which, as we know, TPP might force to change). But that's another story...