In the 80's TV show Miami Vice, the main protagonists took all types of cases - drug dealing, murders and even protecting celebrities. But isn't there a separate police department that deals with murders (as shown in Dexter TV series)? And isn't it DEA who deals with drugs (as shown in Breaking Bad)? There was even an episode where Tubbs and Crockett went to Colombia to disarm the cartel. Isn't it CIA's job?
I don't know about the 80s, but in Dexter (2007) it is shown that vice department deals mostly with prostitution - as Debra was an undercover prostitute. Did the vice department really have so many competences in the 80s?