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What was the deal with the liquidy mirror in M1 before Neo got unplugged? Did he have to touch that to get out of the Matrix? Was it just to show that the Matrix's rules of physics didn't exist?

This bugged me for a long time, but I believe the answer can be found here. http://www.knowthematrix.com/
There is a section about when Neo first touched the mirror. According to article, the red pill disassembled Neo's code. When he touched the mirror, part of the mirror's code implanted itself on Neo and began to corrupt his code. I hope this helps.

Then the machines noticed that something was wrong and ejected him

That's good enough for me

The pill made Neo "undesirable" and ejected him. The water he was dumped into, according to that article is acid that liquifies the dead to feed the living. That's why Morpheos pulled Neo out right away.
Also, if Tank Apoch took too long to find Neo's body, the mirror's code would of taken over Neo's body.

I'm continually baffled by this section of the forum......

ok, the mirror had nothing to do with it, it was a hallucination of Neo's. It had nothing to do with setting him free, or disrupting his input/output carrier signal. It was a hallucination. The Wachowski bros said so. Also, it is used for two things. 1) to remind us of Alice in Wonderland, in that she had to go through the looking-glass (mirror). 2) It shows a foreshadowing of Neo's purpose, his ability to rewrite the Matrix as he sees fit.

I like that one better. When you can't explain it with science, blame it on drugs (it was a hallucination-get it?)

my theory is that his digital self and his real world body are experiencing the waking up process. He says its cold, I'm thinking the liquid in the pod is cold... I think its like what is happening in the real world is happening to him in the dream world, except of course in the dream world the experience of what he is seeing, smelling, tasting and hearing is related to the dream world , but the touch is the same in both worlds, the cold sensation. That's my theory and i'm stickin' to it!