Your original request for a falsification of common descent has morphed into your current argument that we cannot assume mutations are responsible for driving evolution.
It is safe to assume that the phenotypic differences between organisms is due to mutation. An example of this are a group of genes found in virtually all multicellular organisms called the Hox cluster. This locus is a major determinant of the overall body plan of the animal. It looks like it went through several duplication events throughout evolutionary history. This is still an area of active research, but where it has been tested, the mutations to the Hox cluster have been experimentally verified to be responsible for the visible changes of the organism (i.e. more legs, wings etc). There are many other genes that are common to different critters where it can be showed that the specific mutation involved leads to the change in phenotype.
Actually, all I said was: 'Regarding the claim that "all life on earth is descended from one (or very few) common ancestor(s)" -- how is that falsifiable?' Your response has been roughly "well, the DNA is related, ergo they have only one (or few) common ancestors." The counter to that is that it may well be turtles all the way down, if you get the allusion.
It is safe to assume that the phenotypic differences between organisms is due to mutation.
That is the point. You assert it is safe to assume that. I assert there is a lack of proof, and therefore it is not safe to assume that.
Science is not about assuming, it is about proving. So no, it is not safe to assume such a thing. If there were no phenotypic differences then all animals would be the same. To be different, there have to be both phenotypic and genetic differences. So no, your statement is a tautology which says 'if we assume evolution is true' then mutations are the cause of phenotypic differences. There is no proof of that.
. An example of this are a group of genes found in virtually all multicellular organisms called the Hox cluster. This locus is a major determinant of the overall body plan of the animal. It looks like it went through several duplication events throughout evolutionary history. This is still an area of active research, but where it has been tested, the mutations to the Hox cluster have been experimentally verified to be responsible for the visible changes of the organism (i.e. more legs, wings etc).
That is not correct. It is again saying that if evolution is true, those changes are due to mutations. You and evolutionists seem to forget a very simple thing, the phenotype of the organism has a purpose and has to be in accordance with other parts of the phenotype (what we see - arms, legs, etc). It is not there due to luck. The problem with the Hox genes and evolution is that they are not what is important when it comes to development. It is the program controlling development that matters because everything has to be done in proper order. Each time you make a cell for example you have to make sure it is able to get nutrition, oxygen, be able to excrete wastes, etc. So changes to the phenotype cannot be made stochastically (at random) they have to be properly programmed to be in accordance with all the rest that is going on in the organism's development.