the matrix - Was Neo dreaming when Agent Smith interrogated him, his mouth disappeared, and a robotic insect crawled into his belly button?

This is the scene I'm referring to. Right after Morpheus calls Neo and Neo gets captured while trying to escape the Agents at his office building, we see Neo in an interrogation room with Agent Smith. He (somehow) makes Neo's mouth close, and releases a rather disgusting robotic insect that crawls into Neo's belly button. Neo then wakes up, as if from a dream, in his bed at home.

We assume that Neo getting kidnapped is "real" (that is, taking place within Neo's Matrix reality, and not occurring within a dream of his) because we see Trinity outside of the office building as Neo is getting shoved into a car by the Agents. She's clearly worried that he's getting kidnapped, but the only person that notices her is Agent Smith (and not Neo).

If this was a dream (and then the next scene in the dream is the interrogation and Neo waking up), then why the scene with Trinity? Was Neo really dreaming in such detail that Trinity sighed with exasperation from afar as he was being taken away?

But if this wasn't a dream, then what is Neo waking up from? Or did the interrogation even happen? So confused!

Answer

The fact that slightly later on in the film when Neo is taken by the Redpills when driving in the car and the bug is actually removed shows that this probably was a real experience (real in the sense that it happened in The Matrix)*.

As pointed out by Jason Baker, it is possible for the Agents to change the Matrix in real time, explaining how Neo's mouth could be 'removed'. This is supported slightly by the Matrix Wiki where the page on Agents explains the following:

Agents possess extraordinary powers to manipulate their surroundings

Now, although they have limitations, considering their function is to:

eliminate anyone or anything that could potentially reveal the truth of the Matrix to its inhabitants or cause harm to its system

and the fact that they can take-over anybody within the Matrix to achieve that end, it is quite reasonable to expect that they had the power to manipulate an individual's physical (well in the Matrix at least) make-up. It is important to remember that Neo at this time wasn't a Redpill, but a Bluepill, so the effects of the Matrix were still very real to him.

*If you take the view that all the events that occur within the Matrix aren't real, but are like dreams then, yes, Neo was dreaming when that occurred, but for the purposes of this answer it is assumed that actions within the Matrix are not considered to be dreams