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.
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 rapes and homicides, with a few kidnappings thrown in. These cases, if not plea bargained, are seldom heard in less than a year after the event.
Multiple cases are shown which have interstate or international components. While NYPD SVU detectives might cooperate in those cases, they would primarily be handled by the FBI or some other federal law enforcement agency.
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.
When the Police need to arrest a medical professional, they are frequently shown barging into his/her office, exam room, or even the operating room. This would never happen in real life and is strictly forbidden, as it is a gross violation of the patient's privacy, and in the case of the OR, could contaminate the sterile environment, thereby jeopardizing patient safety as well.
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.
The same detectives are seen dealing with both the rape victim and the lead suspect, this would never happen in real life for the fear of forensic cross-contamination (forensic material being transferred from one to another via the hands and clothing of a third party).
When the detectives want to "bring in" or "pick up" suspects witnesses for questioning, they are usually located instantly. That might work if they had a consistent schedule they followed faithfully every day, but few people do that. Even with the invention and advancements of GPS and smartphones in later seasons that would make it easier to locate suspects, it should not be as simple as is shown in the series. Especially as many of the people they are looking for are homeless or otherwise itinerant, and even they don't know where they will be tomorrow.
Some of the suspected criminals are shown fleeing or attempting to flee from the Police (or even during the trial itself) in a way which will ensure that they will be caught. As they try to leave on buses from The Port Authority, when there are several dozen areas around the city where a bus or train can be caught that will take you out of New York City.
Despite many of the crimes being homicides in addition to being sex crimes, homicide detectives are not shown to have responded to the case. The major crime would be the murder itself, with the sex crime elements being included offenses.