Have you considered the salts found in serum when calculating the annealing temperatures of your primers? 

I´m agreed with previous answer by Nathaniel E Wiest. Most of DNA extraction protocols use white cells nucleated DNA from blood collected with minimal quantity of EDTA as anticoagulant. In the case of some microorganisms (mostly viruses) to be identified in serum the sample of choice is blood serum obtained from a the clear (not hemolized) supernatant of cloted specimen. In that case salts could interfere with further extraction and amplification process. Then you shoul select the best protocol for your scientific question since the extraction procedure and then also for PCR or RT-PCR protocol.

Maybe it's like the colleague says , the use of any anticoagulant would no longer be plasma and serum but that could inhibit polimarsa since most chelates calcium. Mineral used by the taq as cofactor . On the other hand the marked hemolis or lipemia also inhibit the polymerase . Therefore it is sampling , and quality are as important as the extracion or PCR protocol