I guess I'll take a crack at this. I think the agents wanted Morpheus. Bugging Neo was just an attempt to see if he would lead them to Morpheus. They need Morpheus more than Neo, because Morpheus has the bargaining chip for the machines. He knows the location of Zion.
This explains why they don't care about Neo.
"Agents control humans, because the humans that are being taken over
want to be controlled by the Agents".
Morpheus never said people want to be taken over by Agents. He explains that the people who are still connected to the Matrix are a threat, because they could be taken over by agents (since they are hardwired to the system) or they could be trick with a story like the one they try to fool Neo with. The whole "Morpheus is a terrorist" and you would be help us out is a Patriotism toward your country type of thing.
I have to agree with Simon when he said:
"But I would add that taking over a human (by a Agent) is not standard
procedure : in the movies, it only happens in a crisis situation.
Maybe it means the loss of a human, and the point of the Matrix is
keeping humains alive, so from a computer point of view, the pros must
be superior to the cons. It's like a escalation privilege : you don't
do it if you could avoid it."
I can't not think of (off the top of my head right now) where at some point an Agent left a human body, and that human host was still okay. I think taking over a human body would kill the host, which is why they don't have millions of agents just jumping in and out of human host.
"Firstly, I don't think weird things trigger a red flag for agents"
Agree. I think that since the machines cant occupy humans without killing them, they depend on Matrix civilization for information. The "machines" are the government. They are "Big brother". When someone reports, like a 911 call, the machines monitor it. When they get reports of someone jump buildings ( would be rare i would think), they would send agents to check it out. They could also put people like Trinity on terrorist list so if they are spotted, people could report them. I think this because in the first Matrix, the agent tells the officer you were given specific orders not to enter the building and wait for the us to show up. Office just tells him to screw himself and that they could handle one women. This hints to me that they depend on the humans for information about these "red flags"