Understanding sources of electromagnetic interference are important in designing any electronic system. This is especially true when combining positron emission tomography (PET) and magnetic resonance imaging (MRI) in a multimodality system as coupling between the subsystems can degrade the performance of either modality. For this reason, eliminating radio frequency (RF) interference and gradient-induced eddy currents have been major challenges in building simultaneous hybrid PET/MRI systems. MRI requires negligible RF interference at the Larmor resonance frequency, while RF interference at almost any frequency may corrupt PET data. Moreover, any scheme that minimizes these interactions would, ideally, not compromise the performance of either subsystem. This paper lays out a plan to resolve these problems. A carbon fiber composite material is found to be a good RF shield at the Larmor frequency (300MHz in this work) while introducing negligible gradient eddy currents. This carbon fiber composite also provides excellent structural support for the PET detector components. Low frequency electromagnetic radiation (81kHz here) from the switching power supplies of the gradient amplifiers was also found to interfere with the PET detector. Placing the PET detector module between two carbon fiber tubes and grounding the inner carbon fiber tube to the PET detector module ground reduced this interference. Further reductions were achieved by adding thin copper (Cu) foil on the outer carbon fiber case and electrically grounding the PET detector module so that all 3 components had a common ground, i.e. with the PET detector in an electrostatic cage. Finally, gradient switching typical in MRI sequences can result in count losses in the particular PET detector design studied. Moreover, the magnitude of this effect depends on the location of the detector within the magnet bore and which MRI gradient is being switched. These findings have a bearing on future designs of PET/MRI systems.