Alexandra Eames routinely wears her hair long and high heel boots. Neither would worn by a female police officer working the streets as they could allow them to become injured by a suspect or during a foot chase.
The detectives often discuss elements of their cases openly in front of people who they have just questioned. This would not occur in real life as they would risk having the person who overheard them potentially contact someone who might be a suspect.
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.
The detectives sometimes pick up a weapon with a handkerchief or by inserting a pencil in the barrel. In real life, the handkerchief might contaminate possible DNA evidence, and the pencil would destroy microscopic markings inside the barrel, making it difficult to match the weapon to slugs retrieved from a victim's body or a crime scene. Instead, one expert recommends holding a weapon in place with gloved fingertips and sliding a thin, stiff sheet of plastic beneath it.
When the Major Case Squad is 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.
When witness or suspects are brought to One Police Plaza and interrogated by the Major Case Squad 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 cop car.
When the Major Case Squad needs 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.
We see the Major Case Squad arrest wealthy people going about their business and when taken down to One Police Plaza they actually cooperate with the authorities rather than allowing their attorneys to speak on their behalf. In real life this wouldn'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.
Some of the suspected criminals are shown fleeing or attempting to flee from the investigators in a way which 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.