It's interesting that Okazaki fragment is able to not get lost in the process of DNA replication and become oriented perfectly in the newly synthesized DNA strand. There must be a series of cellular machines that keep this in the realm of possibility. However, I would assume that a good amount of the DNA errors that do occur are related to the Okazaki fragment, since the process is considerably more complex than synthesis of the leading strand (at least conceptually).
This is really an amazing mechanism that happens within our bodies and within all other eukaryotic organisms. I wonder how the DNA polymerase is able to make the conformation shift to compare the newly synthesize strand to the original. Perhaps a ligand or even a phosphate group binding leads to the action of DNA polymerase. Also, this is far from the only proofreading mechanism that exists for DNA replication, which explains the incredible accuracy exhibited by the complex over the huge magnitude of DNA replicated.
Since this reaction requires a considerable amount of free energy to occur, it must be couple with a different process in the cell in order to be thermodynamically possible. Endothermic reactions like this need to be paired with an exothermic reaction to make the product formation favorable. All reactions need to have a negative change in free energy, the process of making that happen is called metabolic coupling.