I'm assuming you mean "analog" in the purest mathematical sense, because
analog computers (in the ordinary not-explicitly-digital sense) have
been around for decades. Dalmo Victor made a very nice one in the 50s.
> 1) Matter, energy, momentum, spin, and electrical charge are all
> unquestionably digital, they come is discrete package. It could well turn
> out that space and time do too. When you build your analog computer you
> must make use of all these things.
There is currently no evidence that gravity or time are discretely quantized.
> 2) An analog computer MUST have an infinite number of internal states, so it
> must be built with infinite precision, but quantum mechanics tells us that
> is impossible.
It says no such thing. It says only that the precision of our outputs is
limited by what we choose to observe--no limit at all on the unobservable
precision, nor is it a contraint on what we may choose to measure.
> 3) If your analog computer is operating at any temperature above absolute
> zero (and it will be) it will be subjected to thermal vibrations further
> reducing it's precision.
Unless those thermal vibrations /are/ its computational facility.
> 4) Unlike digital machines, any errors in a analog machine are cumulative.
> This is very serious in all but the simplest calculations.
This is true to an extent, but negative feedback mechanisms for error
correction are possible in the analog domain.
Your concerns are not unjustified, but it would be terribly premature to
dismiss the possiblity of analog computation this early in our
understanding of physics.