The uniforms

Anton Diffring who plays Col. Kramer is wearing field grey Waffen SS uniform. Ferdy Mayne who who plays General Rosemeyer is wearing field grey army uniform so these are both correct.
As it has already been said Derren Nesbitt's character is Gestapo and he wouldn't have normally worn SS uniform, they usually wore civilian clothes, but if he did it would be the field grey SS pattern but without the SS runes on the collar tabs- the tabs would be plain black.
The black SS was a parade uniform rarely worn during the war- the obvious exception being the guards at the Reichchancellerie which are shown wearing it with white gloves.
The reason Von Hapen wears it in the movie?- Simple, first it clearly marks him out as a villain and secondly, as someone stated at the time "Because Derren looks damn good in it!"
Ironically, Derren Nesbitt is IIRC Jewish!

Trust me. I know what I'm doing.

As far as I can remember without watching that part of the film again, the jump wings Schaffer wears on his Class A coat during the briefing session flashback are basic parachutist's wings, not senior wings, which have a star on top of the badge's parachute canopy.

Although correctly identified by the poster as not having been in existence in World War II, senior parachutist's wings are awarded to paratroopers after 30 jumps with additional qualifiers during those jumps, one of which is having served as a jumpmaster.