When Harm visits Palmer in prison, the warden assures Harm that Palmer has no connection to the outside on the computer. However, Palmer claims to have downloaded the op-ed from the newspaper (as was confirmed by Agent Nichols). That would only have been possible if he had a connection to the outside to get to the newspaper website.
Col. MacKenzie first stores the frozen sperm in the JAG kitchen refrigerator and then in a home freezer. Neither would be cold enough to preserve the sperm at liquid nitrogen temperature.