-Microwave radiation is non-ionising and cannot be used to trigger changes in the chemical structure of DNA.
-Agent Einstein claimed that you cannot deactivate immune functions by adding something to the genome, only by taking something away. I can think of several ways this could be achieved. A gene encoding a protein which binds to and inactivates immunoglobulin would be a good one, or an inhibitor for any one of the proteins involved in the complement cascade. The human genome already has plenty of genes coding for immune inhibitors, a mere alteration to the promoter sequence for the gene encoding C1 esterase would probably be enough to scupper the whole complement system.
-Live vaccines are attenuated, so they shouldn't be able to cause full blown disease symptoms even in immunocompromised patients.
-Einstein told Scully to centrifuge the alien DNA she'd isolated via gel electrophoresis, when in reality they'd have had to centrifuge the original sample before electrophoresis.
-Scully told Einstein to amplify the alien DNA via PCR using primers taken from the sample itself. This wouldn't work. You'd need to use primers corresponding to sequences either side of the DNA you wanted to amplify.
-Even once they had the DNA they needed, they'd have needed to use a vector to get it into the cells of patients. Presumably this would have to be a vector which targeted the precursor cells of the immune system found in the bone marrow, although that would depend on the exact mechanism by which the 'spartan virus' fucks up the immune system. But there was no mention of a vector, it looked more like Scully was just running around with a bag of DNA to pump straight into people. This stands about as much chance of working as trying to program a computer by emptying a bucket of floppy discs over it.
-Vaccines don't alter your DNA. A virus or virus-like vector packaged in with the smallpox vaccine could, theoretically, but probably not in a targetted way. The vector would therefore cause random knockout mutations, leading to a marked increase in cancers amongst other things. I know of no association between smallpox vaccination and an increased incidence of cancer.
-Scully apparently has 'extra nucleotides'. Human DNA contains only four types of nucleotide, if she did have extra ones her cells wouldn't know what to do with them. Most likely the introduction of any foreign nucleotides would lead to apoptosis, programmed cell death, and if these nucleotides had been introduced to all Scully's somatic and germline cells then that would mean a very dead Scully.