In the double-slit-experiment, one particle at a time (for example, the double-slit-experiment performed by Dr. Tonomura showing the build-up of an interference pattern of single electrons) can be observed in a detector or photographic plate by attenuating the source. At such a low rate of detection, I read that background radiation becomes a significant proportion of the particles detected. What I don’t read, is the effect virtual particles have on this experiment. Should they be factored into the experiment? If so, or if not, why?
The question implies that you don't know what virtual particles are. The name 'virtual particle' is arguably a bit of poor terminology. It refers to a disturbance in the field (for electrons the Dirac field, for photons the electromagnetic field) that is part of the complete calculation for how a particle moves from one place to another or interacts with another particle. The 'virtual particles' are a convenient way to break up a calculation into a sum of lots of pieces. Asking whether they influence things is sort of muddled because they are the influence (or part of it) when fields interact.
Two-slit experiment is a thought experiment to demonstrate the wave nature of electrons in quantum mechanics. There exist many implementations of this experiment, which necessarily differ from the simple analysis given in the textbooks and compounded by many external influences, than need to be factored in.
E.g., observing electron wave interference in nanoscale Aharonov-Bohm rings is complicated by phase rigidity due to multiple scattering events. This necessitates opening the interferometer in order to allow scattered particles to escape, which necessarily lowers the visibility of the interference picture. In a way, this is just the opposite of the problem that you have in mind.