Right after Ryan dies, Stabler is talking to the captain. IAB shows up and takes Stabler to interview him. In the interview (which was very shortly after the attack), Stabler's voice is notably hoarse, and even slightly nasal, suggesting the scene was filmed when the actor had a cold.
In the episode Burned (2007), Elliot Stabler is shown to be clearly living in an apartment building as a result of the separation from his wife. There is a buzzer on the right at the landing and the large window in the front door shows a small alcove with a second security door leading into the building. However, in this episode, his front door opens right onto the street with no buzzer visible and Dr. Warner knocked on his front door without having to be buzzed into the building.
In a real situation, if a suspect stopped breathing in the course of an arrest, officers would continue CPR until EMT's got there. The officers would not know what caused him to stop breathing; knowing Ryan was a heavy drug user, his death may have been caused by drugs or even a heart attack due to drugs and the exertion of running and resisting arrest.
Olivia says to Tucker that she and Elliot had been partners for 8 years. However, when the series first began, it was said that they were already partners for about a year and a half. Also, in the 9th episode of the series there was a 6 month time jump. Thus, they had been partners for about 10 years at that point.