Do you mean evolution as a history, or evolution as a specific set of explanations in the realm of molecular biology and game theory? I have no trouble admitting that biology has no complete description of the sources and processes of mutation.
But I do believe that selection is adequate to explain which changes survive. I have been posting this over and over for several days now, but will try one more time. Darwin did not discover anything about the cause or nature of mutation. He really threw up his hands at trying to explain the mechanism of variation.
What Darwin revealed was the process of selection, which shapes life over the long run. Selection is an observable phenomenon. It is amenable to experimentation. In fact it was artificial selection that suggested natural selection.
If you believe there is some miraculous computer program setting up specific changes in the genome -- whether these changes are determined by initial conditions, or twiddled with on the fly -- selection still shapes life. The final arbiter of good design is survival and reproduction. This is true in biology and it is true in the marketplace (where everything is presumably designed, but chaotic and indeterminate forces -- the invisible hand -- shape things in ways that are beyond the control of mere inventors).
But I do believe that selection is adequate to explain which changes survive.
And yes, you are correct, my objection to the theory of evolution is that the "random mutation" part of the formulation is either or both not adequate/incomplete. The good news is that a lot of scientists and mathematicians are working on it!
But, for the record, this is the also the main thrust of the Intelligent Design argument - that the evidence speaks against happenstance and for a directed, purposeful or orderly mechanism. But, again, Intelligent Design "theorists" do not identify the source of that direction - whether God, cosmic ancestry, collective consciousness, etc.