The piece of torn paper plate upon which Julian wrote his number is about 1/5 the size of the piece she pulls out of her pocket when she calls him.
After finding Ramzy's address is near Battery Park, where he killed himself, Lizzie tells the bomb squad not to leave, because they'll have to sweep his apartment. She and Dylan enter the flat before a sweep, without any back-up, and without checking the door for booby-traps, which would be S.O.P. with a bomber of unknown affiliation.
Lizzie and Dylan discover there is a second bomb due to go off in 15 minutes, at 16:21, in Central Park. They're in an apartment located walking distance from Battery Park, which is at the southern tip of Manhattan. The two parks are separated by approximately 100 blocks in the most congested city in New York. There is no way, even on Dylan's motorcycle (which is back at Battery Park) for them to get to the Central Park Bandshell and be conducting their search in 15 minutes.
Knowing there is a bomb probably being detonated in Central Park, S.O.P. would have been for Lizzie to mobilize every cop in the vicinity to blanket the area and look for suspects, but she is the only officer there when the bomb goes off.
For the 3:08 bombing at the fountain, Lizzie and Dylan hear the nearby explosion, and run for the stairs. As they round the corner, still running, and come into view of the bomb site, the body is already being covered with a sheet, the crime-scene tape is already up on the sidewalk across the street, and the bomb squad commander has already determined that the bomb was identical to the others they've investigated. All of this would've taken from several minutes to an hour to accomplish.