What is the significance of the silver goo in the Matrix?

A similar question (about the liquid mirror) has been asked at the Sci Fi Stack Exchange. The following, although complete speculation, is from the highest rated answer:

On one level, the liquid mirror is just a manifestation of the dissolution of the fake reality of the Matrix. It evokes a dreamlike quality in keeping with Morpheus' lines during the scene, and also provides an element of growing tension that leads up to the shock of waking up.

This, however, doesn't explain why it's specifically a mirror — a melting wall would do just as well for that. On another level, though, a mirror is a metaphor for both perception and for a boundary. (Note the focus on Morpheus' mirror shades, and on Neo's reflection in them, in the previous scene.)

Before taking the pill, Neo's perception of himself and his surroundings was flawed, like the broken mirror — he perceived the illusion of the Matrix as real. The healing of the mirror is the first step in his beginning to perceive the Matrix for what it really is.

By touching the surface of the mirror, Neo takes a step across the boundary between the Matrix and the real world (there's almost certainly an allusion to Lewis Carroll's Through the Looking-Glass here, just as the previous scene referenced Alice in Wonderland), a step whose irreversibility is shown by the mirror swallowing up Neo completely.

Finally, there is a school of thought on several online forums which argues the entire scene is a little out of place with the movie and was only included as a reference to Alice in Wonderland:

You take the red pill, you stay in Wonderland and I show you how deep the rabbit hole goes.

The second Alice book was called Through the Looking Glass. This is exactly what happens to Neo. He literally goes through the looking glass, i.e. mirror, as it engulfs him completely as begins his journey to the real world.

Echoing my answer to a similar question on Scifi:SE, the mirror itself is just a mirror. The fact that it fixes itself, flows and melts is merely a result of Neo's hallucination.

In this rare webchat, the Wachowskis gave us some additional info about the mirror scene.

ThedrickFel: What exactly was the mirror made of? Was it the same stuff they injected into Morpheus? Why silver?

WachowskiBros: The mirror is actually a mirror. When Neo sees it it’s a hallucination, but it’s the direct result of the pill Morpheus has given Neo. Reflections in general are a significant theme in the film. The ideas of worlds within worlds..

As Omegacron pointed out in his comment below my other answer, this also explains why no-one notices or comments on it. It's solely Neo's perception that anything has changed.

The whole purpose of making Neo in the Matrix get coated in the silver goo is to trace the location of his real body.

Morpheus: The pill you took is part of a trace program. It's designed to disrupt your input/output carrier signal so we can pinpoint your location.

Mirror is how humans see their real self, for us a mirror speaks the truth. Psychologically, it confirms a lot about our existence, appearance etc. When a mirror goes psycho on you, it perhaps helps the brain go nuts to generate the required signals which will be loud enough to trace the actual body of Neo.

In my opinion (and this is only my opinion and not backed by facts or director's commentary), the "goo" is the mirror. It's just the mirror melting, and when he touches it, the "goo" begins to cover his body. I think this was done to reflect a dream-like-yet-wide-awake state, similar to an acid trip. If you've ever done any type of psychadelia, perceptions like this are common. This type of perception is even quite prevalent in cartoons from the 60's and early 70's, where one form morphs into another, into another, into another. It was just a way to show the "real" world fading away into the world of the Matrix, and the morphing from one to another. Why do you think Morpheus is called Morpheus? ;o)

Read the book "True Hallucinations" by Terence Mckenna, he goes into a phenomenon that happens while on ayahuasca where the body oozes a goo similar to the liquid mirror in the movie. He describes this goo ass pure consciousness manifested into the 5th dimension thats only visible on tryptamine drugs. He also goes into how shamans in the Amazon use this goo to heal people and do see into the 4th dimension. It's an awesome book but it takes a very open mind to read.