Elise's ID shows her name as Elise Smith, her name is actually Elise Taylor. It also states that she is a Special Agent when in fact she is an Analyst.
An FBI subordinate is not required to follow an order which they know to be unlawful. As such, the order not to follow the suspect given by the female supervisor could be disregarded.
The bomb displayed had the bricks of C4 with exposed blasting caps. There were no trigger wires on them other than the two wires needed to detonate them. Disarming the bomb would be a simple matter of removing the blasting caps.
A suspect is identified at the plaza, and instead of making a covert take down, they call to her from a distance, which results in a foot pursuit. This is a typical TV cop error for entertainment purposes.
On several occasions, characters are shown using either a radio or a cell phone (which is a radio) around explosives. Experienced agents would know not to do this, as radio frequencies can set off explosives.