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It could be falsified in a number of ways: finding organisms that have radically different genetic codes, or finding that biochemical analysis did not produce a tree structure, or that different analyses produced different trees.

You do not need radically different genetic codes to show others could not have descended from it. The reason is this - to change the genetic code, one single reading, you would need to AT THE VERY SAME TIME need to change the DNA bases of all the genes using that code or the organism will not function. So what you need is a miracle or a designer and evolution says there are no miracles and no designers. So yes, that proves the theory of evolution to be false (at least in regards to the statement that each and every species descended from another species). But then if not all descended, then there must have been a Creator at work eh?

The reason is this - to change the genetic code, one single reading, you would need to AT THE VERY SAME TIME need to change the DNA bases of all the genes using that code or the organism will not function.

Not really - the few cases where the 'dialect' of the genetic code differs are bacteria, some of which also use amino acids no-one else does. If a particular codon codes for two different, but similar amino acids (eg, both small and hydrophilic), (this could come about via a mutation in the genes for the particular t-rna), the organism could very well survive with an *ambiguous* genetic code, since the proteins produced by either reading would be similar.

There's no reason such a code could not be 'frozen' at a later time. See Watson (or is it Crick - I don't have the book in front of me, and Amazon is down for maintainance) in Mark Ridley's book "Evolution" (very highly recommended; among other essays, it include the original research on sickle-cell, and also Dobzhanski's classic "Nothing in Biology makes sense except in the light of Evolution")

But then if not all descended, then there must have been a Creator at work eh?

How does this follow? It is possible there were at one time several kingdoms of bacteria with similar but not identical genetic codes that arose independently from the precursor chemical evolution. (If the chemicals are the same, but the code is different, they're still edible) No-one knows at the present time.

The base of the phylogenetic tree may not in fact be a tree, since prokaryotes share dna across 'species'. (Once you get to multicellulars, it does seem to be a tree)

AFAIK all animals, plants and fungi use the same code; I'm not sure about protoctista.