Evolution's mutation mechanism does not explain how growth of a genome is possible. How can point mutations create new chromosomes or lengthen a strand of DNA?
I'm tired and sick here so I have no idea right now. And I doubt either of us has enough high-end education to answer this thoroughly without chucking links back and forth. lol Even if I did, I bet any creationist reading this would keep moving the goal-posts and pull more of the "god did it!"
Wow! I missed a lot of posts. Yesterday I was looking up information on a college, and today I was actually at the college scoping them out to finish my (Biology) degree.

As for this, point mutations do explain both new chromosomes or the lengthening (or shortening) of DNA.
There are several types of point mutations. The smallest are base-pair substitutions; which change one pair of nucleotides with a different one. This can cause that particular section to produce a different amino acid (but it may not, many amino acids have many possible nucleotide combinations). It will usually lead to a protein that is useless or less effective, or rarely lead to a better functioning protein; it's typically the mildest of mutations.
Insertion and deletions are the additions or losses of nucleotide pairs in a gene (lengthening or shortening). These can have a devastating effect if they are near beginning sections of a strand, as they alter the amino acid codes of every part of the strand after it (the mutation).
Mutations occur in about 1 in every 100,000 genes per generation, and that change is passed on to the next generation of cells. It doesn't seem like many, but with the number of replications that occur at the cellular level, it occurs quite often. It's why single-celled organisms can adapt so much faster than more complex organisms; any mutations are passed on to the next generation of single-celled organisms, while multi-cellular organisms require a mutation during the creation of gametes (reproductive cells) for the mutation to carry on to the next generation.
This also answers the question about chromosomes, as chromosomes
are the DNA. Chromosomes are the condensed and duplicated DNA strands, only appearing during cell replication.
And for chromosomes, they have their own special type of error called nondisjunction, where the homologous pairs of chromosomes fail to split apart during anaphase I of mitosis, or the sister chromatids fail to split in anaphase II of meiosis. This leads to one cell with two sets of an identical chromosome, and one cell missing a chromosome. Nondisjunction occurs very frequently in meiosis, but usually the results are so devastating in developing zygotes that they tend to miscarriage very early in a pregnancy.
Some of the disorders caused by nondisjunction: Down Syndrome, Turner's Syndrome
During cell division, pieces of the chromosomes can also be deleted, or broken off and joined with either a different chromosome (may cause errors in gene expression) or the other part of the homologous pair, causing a duplication. Add in the frequent rate of mutation, and that's how the genome managed to grow.
Sorry if this is a bit long-winded; I enjoyed it a little too much.