One of the main problems was that the Abwehr, though nominally the official German military intelligence organization, was robbed of influence because of the existence of the Sicherheitsdienst the security service of the SS, the Reichssicherheitshauptamt (Reich Main Security Office) the intelligence office of the Deutschen Polizei both under the control of Himmler.
On the other hand the Abwehr were according to some historians actively anti-Nazi (cf. H. R. Trevor-Roper (1947). The Last Days of Hitler, pp 24, 27. Davies (2008). No Simple Victory: World War II in Europe, 1939-1945, p. 251.).
Wilhelm Canaris the head of the Abwehr advised Franco not to join the war on Germany's side. (Goerlitz (1985). History of the German General Staff, 1657-1945, p. 384.) Indeed Canaris was involved in what was termed by the Gestapo "The Black Orchestra" ("Die Schwarze Kapelle" ), a conspiracy that plotted to overthrow Hitler. After the famous bomb plot against Hitler failing, Canaris was hanged in 1945.
I have a follow up question to this: How do you know if a country is good at espionage?
I have a follow-up question as well: Is it true that Germans were regarded as very straight-thinking people and more succeptible to "out of the box" espionage? That's the way this BBC Documentary portrays them and describes that kind of more straight thinking by German intelligence as the reason Operations like Mincemeat were successful and I am very curious as to how much it was dramaticized or actually true.