In "The Third Man" it seemed like almost every other person was involved in something shady, especially racketeering. Ordinary people avoided dealing with law enforcement. When Holly discovers what Harry Lime is in trouble for, he seems to be the only character who was genuinely shocked by the inhumanity of Harry's crime. Were things really this bad, or was it exaggerated in the name of film noir?
"Shady" is concept that is hard to work with.
Vienna has been under Nazi rule for 7 years and acted as the Third Reich's second capital; it has suffered under allied (mostly US) bombardment and then under the final battle for Vienna between German forces and the Red Army. Many parts of the city, much of the vital infrastructure was destroyed. Everyone who could flee the city and move to relatives out in the country did so.
The new political situation was less than clear. Vienna was under joint occupation by all 4 allies. The interim government under Renner was installed by the Soviets when they still were the only force in Vienna and it was still unclear if the US would accept it or try to install another government in the western sectors of Austria, possibly leading to a divided country.
Many of the old civic elites were removed, of course: Nazi Police, judges, magistrates had to leave their positions. Some of the pre-war elites were slowly returning from camps of prisons, but the jewish elites were dead or gone (and not necessarily welcome!). You could become a police officer or district governor simply by walking up to the Soviet kommandantura and telling them you're an anti-fascist.
The food and medicine supply was catastrophic. The winters of '45 and '46 saw mass hunger and high death rates, especially for the younger population. Racketeering, "Schleichhandel" or simply "Schleich" was often the only way to obtain many goods and medicine.
So yes, I guess you could say that things were "shady".