Much of the equipment (Big Ed flashlight, style of air-pack mask, etc) carried by Morrison (and other firefighters) in his "early years" as a firefighter was not available until more recent times (mid-'90s)
Ladder 49 clearly has a Federal Q siren in the direct center of the truck. Also it is clear that Engine 33 does not have a Federal Q. In multiple scenes of the movie Engine 33 is arriving on scene and you hear a mechanical siren coming from the truck, such as the apartment fire during the snow. Also even when you see Ladder 49 coming on scene, the mechanical tone sounds nothing like a Federal Q.
In the warehouse with the second victim, Jack gives him his mask to breathe through. When you pull off your mask, you should push the blue button. If you don't, the tube the air goes trough doesn't lock and all of your air goes away. When you put the mask on, and start to breathe, the tube unlocks itself, so Jack should have locked it again when he took the mask back.
When the large explosion occurs while Jack is in the warehouse, you see the floor cave in under his feet, immediately followed by Jack sliding in. In the next close-up scene, Jack is obviously on the slope struggling to stay on that floor and not fall into the newly created hole. In the next scene, you see the floor is again whole, then caves in, and once more you see Jack start to slide down the angled floor toward the hole.
When Jack is lowering the victim from the warehouse in the beginning of the movie the rope is wrapped around the metal construction. However, when the explosion occurs to his side we can see that the rope is no longer wrapped around the metal but simply lying across it.
At the beginning of the movie, Jack is carrying a red bag which he puts down when tending to the first found victim. After having the other firefighters carry him down, the bag reappears when he is going after the second victim, but he never picked it back up.
When the trucks are responding to the fire during the snowstorm there is an overhead shot of the trucks going down the street. In that shot, you can see that Ladder 49 is a more modern Pierce tiller ladder but then it switches back to an older Seagrave tiller ladder.
When Jack, Linda, Dennis and his date are at the bar at the beginning of the movie, Dennis and his date get up and leave the scene to go smoke outside. When Jack is talking to Linda, her hands repeatedly change positions on her drink from being on the glass to her straw.
After Jack falls, the scene is he's laying on the ground, P.A.S.S. device (the yellow device with the flashing lights on his belt) is sounding and you can hear dripping water in the background. In real life the pass device is so loud, it would be the only sound you could hear if you were next to it.
Capt. Kennedy orders all exterior operations shut down to execute Jack's rescue. In real life, all operations would be continued and a Rapid Intervention Crew (R.I.C.) would have been activated to execute the firefighter rescue.
Throughout the movie, Captain Kennedy is running the rescue operation of Morrison. That task would have been left up to a Operation Section R.I.C. Division Leader, Command would have only been given updates through the Operation Section Chief.
When Chief Kennedy is talking to trapped Jack Morrison on the radio from outside the building, when showing Jack trapped in the burning building, the type of radio Chief Kennedy is using changes multiple times. Sometime Kennedy is talking on a portable radio with no mic attached to it, and sometimes he is talking on a portable radio with a speaker mic attached to it, and is holding the mic in his hand. However it is common for the BCFD to run on both a TAC channel and the communications channel therefore causing a chief to have 2 radios.
When Jack is on the rope holding the man at the city high-rise fire, you hear a news chopper saying that it is over the fire scene, but after Jack says that he will drop the man if he doesn't calm down, you can see the word "POLICE" on the bottom of the chopper.