Decker had found that the transporter mechanism modules were "faulty". Under normal circumstances, maybe, he would have immediately notified Starfleet but Kirk interrupted the scene and distracted Decker. Odd thing that nobody else felt responsible to do something about it.
Curiously, when I read the thread title I was thinking that Kirk's takeover of the transporter room controls could have contributed to the accident.
The scene is one of the weakest points in the film. Kirk had been a paper pusher for approx. 2.8 years at Starfleet and suddenly he thought he could do a better job than the transporter specialist, Janice Rand probably was at that time.
Entirely possible that Kirk only made matters worse in the transporter room than being of any actual help (OTOH this set the theme for his next screw-up).
Bob