The time-lines of trials seem to be rushed and take place within days of the crime. Most of the cases on this series are homicides and these cases, if not plea bargained, are seldom heard in less than a year after the event.
When witness or suspects are brought to the station and interrogated sometimes it's pretty clear they didn't want to come. If there is no probable cause for an arrest or an active arrest warrant, the police can't make you go anywhere against your will. Once in a while, a wealthy or educated person will assert this, but mostly the cops just walk up to people, put the cuffs on them, and place them in the car.
In real life, the same group of police officers working with the same group of prosecutors in one year is highly unlikely. Also the same could be said of the police and prosecutors getting through the number of cases they are shown to in a year's time-frame.
When the detectives want to "bring in" or "pick up" someone for questioning, the subjects are usually located instantly. That might work if they had a consistent schedule they followed faithfully every day, but there are few people who do that. Also, many of the people they are looking for are homeless or otherwise itinerant, and even they don't know where they will be tomorrow.
We see the detectives arrest wealthy people going about their business and when taken down to the precinct where they actually cooperate with the authorities rather than allowing their attorneys to speak on their behalf. This doesn't happen as wealthy people who aren't flight risks are allowed to surrender rather than be arrested in public and will let their attorneys do all the talking.
The series makes it seem like the prosecutors and defense attorneys are evenly matched, which is way off. Lots of defendants can't afford a lawyer and are assigned, public defenders. Public defenders can be tasked with 500 cases in a year. (And that's a conservative estimate.)
In-trial pleas or deals would be extremely rare. Once the trial starts, the state would have little incentive not to go for the maximum penalty; the time and resources for the trial have already been allocated.
On more than one occasion, a suspect has invoked his/her right to counsel and yet the officers continue to talk with them. If the suspect goes to court this will usually come back to haunt the detectives as the defendant's lawyer will throw out any statements made by their clients. However, if the suspect is innocent then the police will usually get away with talking to them without a lawyer present.
Though it's more common for detectives to have many cases open and working at a time, and may devote a few minutes or hours to several over the course of a single day, having them give 100% of their time and attention to a single case every week is a storytelling practicality; given the show's two-part format, a compression of time is necessary in order to fit everything into 45 minutes.
When the detectives are interviewing someone or working a crime scene, they are never seen taking notes. Real detectives are constantly taking notes. The notes are so important that they are occasionally booked into evidence to ensure the originals will be available for review before trial.