We study the impact of residual radio frequency (RF) impairments and fading on the spectrum sensing performance of a classical energy detector (ED), which is employed in a full-duplex wireless system. Specifically, we present novel closed-form expressions for the false-alarm and detection probabilities, assuming Nakagami-m fading, and the impact of residual RF impairments. The results reveal the importance of taking into account the wireless environment and the ED's capabilities, when evaluating the ED performance and setting its threshold.