If you know what to look for, a lot of the time there are little “tells” that give you a big clue to general accents, even if you otherwise can’t pick them apart (for Austrian, I guess there is the “Hillbilly twang” that others mentioned).
To me, Hitler in the Mannerheim recording just sounds like… well… Hitler. If you ever got him to calm down and have a polite conversation, as opposed to the cartoonish caricature we all know and love of Hitler having private conversations like he’s addressing all of Germany from a podium. For all I know though, this might have simply been the only time anybody ever got Hitler to calm down for a conversation. 
EDIT: Mind you, I don’t know German accents, or even much German aside from a few key useful words like “Panzerschwein.” I just have a general idea of what German sounds like to my ear For all I know, Hitler in this recording and Podium Madly Gesturing Hitler could be as close-sounding in German as Jeremy Clarkson and Slim Pickens in English.