Horizontal gene transfer
Don't expect to have a tree! Horizontal gene transfer happens and therefore we would end up with a network, not a tree.
Different DNA sequences have different evolutionary histories. See, in particular, the question of incomplete lineage sorting. This means that one may compute a tree for a given DNA sequence that must disagree with the tree of another sequence. So, don't expect a perfect species tree where all sequences will agree on.
Note that the two points "Horizontal gene transfer" and "Gene trees" are highly related. So much so that they could fit together.
Not all individuals have been discovered
If by saying
of every organism, you meant "of every organism that we encounter", then we still have the issue of organisms that we have never encountered. If you meant "absolutely every individual that exist", then this is a non-issue. It also matters as to whether you mean every individual of every species or just one individual per species.
Also, it is slightly unclear whether, in your hypothesis, we can sequence all dead individuals! Extinct lineages would still not be resolved if we cannot sequence them.
Massive mutational events
It is possible that very large mutational event could prevent us to see the exact relationship between individuals. But that would only interfere on an extremely fine scale phylogeny (intra-species level).
If we really sample all the individuals, the detail of the methodology may not matter much. It will still need to be decided whether we want to consider
AATC closer to
AA.C or to
. indicates a deletion). Again, this will likely only matter on a very fine scale (intra-species level).
Of course, if we sequence every nucleotide that exists on earth, we would never have the computational power to even store the data. Not talking about actually processing it. We would not either have the computational power to process the sequencing (nor the necessary amount of products to allow for the sequencing to happen).
If you meant to fully sequence only one individual per species (and then again the arbitrary nature of the concept of species will complicate things up), then we might have the computational power (see @KonradRudolf's comment)
The concept of species can often be misleading. You might want to read the post How could humans have interbred with Neanderthals if we're a different species? for a discussion on the concept of species.