There were some - two prominent examples in Adenauer's administration were Hans Globke and Theodor Oberlaender.

Globke had worked within the Ministry of the Interior during the Nazi years, and was involved in the drafting of the Nuremberg Laws, and was high enough in the Ministry to be subject to automatic arrest per denazification procedures. Globke was a key ally for Adenauer as Parliamentary Secretary, and despite some knowledge about his past, he remained in the role until the end of Adenaeur's administration.

Oberlaender was Minister for Refugees in the 1950s, and had been involved with the Lviv pogrom in 1941. He remained in government until 1959 when he was forced to resign when a scandal emerged about this past.

Some discussion about this in (if you have access)
West Germany: A Pre-Election Survey Uwe Kitzinger The World Today, Vol. 17, No. 3 (Mar., 1961), pp. 110-122)
Restoring a German Career, 1945-1950: The Ambiguity of Being Hans Globke Daniel E. Rogers German Studies Review, Vol. 31, No. 2 (May, 2008), pp. 303-324)

Tl;dr: Yes, a lot.

During the Potsdam conference in August 1945 the Allies decided to start a process called "Denazification". However, this process was handled differently in the differenzt occupation zones. There's a pretty good statistic on the way denazification worked in the three western zones: People were put into one of five categories:

I. Major Offenders (immediate arrest leading to capital punishment or (mostly) life long sentence)

II. Offenders (immediate arrest, up to ten years sentence)

III. Lesser offenders (most likely put on probation)

IV. Followers

V. Exonerated (Entlastete)

54% of those tested were classified as followers, roughly 34% weren't classified because the trial was cancelled, 0.6% were acknowledged as opponents of the Nazis and 1.4% were classified as I and II.

The major goal was to get all of those that had worked for and advanced the Third Reich out of decisive positions. However, this soon proved to be quite difficult because so many people had followed and worked towards the Nazi regime - there are only so many teachers, professors, judges, lawyers and bureaucrats capable of rebuilding a destroyed country. Also, those who would often say "I didn't have a choice but to follow my orders before 1945" showed quite a lot of creativity to look like opponents after the war had ended. The term "Persilschein" (Persil certificate, Persil is the most popular german laundry detergent) was a popular way of describing a practice where actual or fake victims of the Third Reich confirmed the innocence of those standing before trial in writing. Others claimed to expect proof of their innocence (e.g. via mail) long enough so that the courts simply forgot about their trial.

So, many people escaped denazification, and a lot of others were put in public positions even though they were classified as Nazis of class II or III. First, because these people were desperately needed, second because others in power managed to get their former comrades jobs. This was especially powerful in institutions that aren't necessarily huge in public. In the 1950s, the Bundeskriminalamt (sort of the german FBI) looked at two thirds of their leading employees being former SS members. The "Organisation Gehlen" and its successor "Bundesnachrichtendienst" (the german foreign intelligence agency) was formed around a core of high-rank Nazis, even in the 1970s roughly 30% of its employees were former members of the SS, SA or SD. In politics, many were at least former party members. Kurt Georg Kiesinger, Germany's third chancellor, was one of those party members and had worked in the Ministry of Foreign Affairs (to be fair, in late 1944 he was denounced by two of his colleagues because he allegedly "obstructed the anti-jewish action").

One of the most prominent examples of an Ex-Nazi holding office is Hans Filbinger, and he's also a good example of the ongoing debate. Filbinger became the Ministerpräsident (a bit like a US governor) of Baden-Württemberg in 1966 and it took time until 1978 when he was publicly denounced as a Nazi military judge who had worked on at least four trials that led to capital punishment. This caused a huge debate during which he had to step down, partly because of a phrase he used in an interview: "What was lawful then can't be unlawful today" (he later said he had never said that).

Later, he founded a national-conservative institute (Studienzentrum Weikersheim) and agitated against "the falsification of german history, the defamation of the german soldier and the glorification of those that defected". And even after those words in 2007, when he died, his indirect successor in office (Günther Oettinger) said in his eulogy that "Filbinger wasn't and had never been a National Socialist - he was a Nazi opponent. But, like millions of other germans, he couldn't escape the pressures of the Regime".