When I watched the 4th episode (the one in which Light learns the name of the FBI agent that was following him) I thought that he is going to do a really dumb thing. By just killing an agent, he would have revealed his identity to a dangerous point. But oh, I was so wrong.
What Kira actually did was the best thing for him to do in this situation (if you can call this massive murder “a good thing to do” at all, even in the context). He made FBI and Japanese police fear him. Fear is his only shield. By making FBI drop the case he dealt with one opponent, for the time being. And the second opponent lost too much man power to be efficient. On the surface of things Kira won the round.
But let’s look at the cost of the victory. He had to concoct that accident in a bus to get the name of the agent. Knowing that Kira can manipulate people, it would not be difficult for L to link the events together. He can find out the time of the accident, he can learn whom the agent was following by that time. That might be gave over for Light. So, the only piece of information that L needs to solve the problem is the fact that his agent had this weird accident in a bus. So basically, if the girlfriend of that agent find a way to contact L, there is a big chance that the mystery of Kira will be solved.
As always, fell free to argue my ideas in the comments =) See you next time (^_^)/
My other posts on Death Note:
Here is the list of all my posts on Death Note.