It is hard to gauge perceptions of people that watch those shows unless of course you took some sort of survey. I suspect that to some degree any audience would be influenced by watching. Some time has passed since I have watched any of those programs but from what I have seen in the past most arrests made are "legal arrests". As a matter of fact, I can't remember a time when I saw an illegal arrest made on any of those shows. A law enforcement officer can affect an arrest if he /she has probable cause to do so. Probable cause is "more than a hunch", it is some articulable set of facts that the officer can describe. Note that it is not based on opinion but facts. When police officer's apply for an arrest warrant they have to be able to describe the fact pattern of the case. When they don't the warrant will be denied by the magistrate.
Indeed, media does alter individual perception on just about every topic. I would say that legal arrests might not make much of a difference. How the media depicts the elements of the criminal justice system impacts greatly how individuals view this system. When confronted with actual arrests, individuals naturally comb their own minds from their own perceptions and experiences with such an event. How the media shows these elements play a large role in how we perceive this reality. When confronted with the truthful elements of such events, individuals might be able to place the media depiction of them in the proper context, but outside of this, there is an effect that the media has in our understanding of arrests, police conduct, and the rights of the accused.
It's difficult to say, since there is no accurate measure of what public perception is. But I think one could safely argue that peoples' perceptions of the law in general, and specifically what is legal and what is not, are often based on what they see on television. Unfortunately such "reality" television often has little basis in reality, and many times people believe what they see in fictional cop shows is real and has a legal basis.
Television in general helps to focus and define public perception, to be sure, but in my opinion it is nowhere near as influential as, say personal experience and family at shaping those beliefs.
I believe it is true that television somewhat shapes public opinion of what is legal and what is illegal and how matters are handled.
Another aspect of this is region. For example, a television show may display certain events which may be handled in a certain way. How it is handled legally may be true in one area but not necessarily another. Basically, laws vary from city to city, state to state, etc.
I do think that it is important for people to realize that what they see on television is usually for entertainment purposes only. Unfortunately, people do not always realize this.
TV and movies have substantial influence on general public perception on what constitutes a legal arrest. Most of the people, not studying law as a profession, do not read the provisions of law either relating to arrest or most of other criminal investigation and judicial procedure. There are very few who are exposed to these provisions through direct involvement in such activities. Thus their main sources for information on such legal matters is what they collect from various general sources. such as, general publications including newspapers, magazines and novels, TV, movies and general discussion with other people. Among these sources the original sources of information of the people discussion is also frequently the other sources listed in the previous sentence. Thus, TV, movies, story books, and newspaper reports form the major source of information on legal provisions for an ordinary citizen.