The cab is shown crashing into an unloaded flatbed truck and instantly exploding into a fireball. While the crash would have been severe, since the truck was unloaded and the cab's gas tank is in the rear, the explosion would not have happened, nor would the fireball. This is a common special effect used for dramatic purposes.
Red tells Elizabeth that "Yesterday in Brooklyn a taxi drove into the back of a truck under the 86th Street "L" train." The train that runs on 86th Street is the "F" train.
NOTE: In talking about the train under which the crash occurred, Reddington correctly refers to it as an "el" (for elevated), not as a line designated by the letter "L."
In the beginning of the episode when Ms. Mitchell gets into the cab, she's picked up at the intersection of Avenue X/86th st and McDonald Avenue (scene is shot from Avenue X/ 86th st). The following scene the cab driver is making a turn onto McDonald Avenue from Bay Parkway, which is north of the previous scene, and is heading back south. The car accident actually happens down the block from where Ms. Mitchell is picked up from.