The O9IV star HD 57682, discovered to be magnetic within the context of the Magnetism in Massive Stars (MiMeS) survey in 2009, is one of only eight convincingly detected magnetic O-type stars. Among this select group, it stands out due to its sharp-lined photospheric spectrum. Since its discovery, the MiMeS Collaboration has continued to obtain spectroscopic and magnetic observations in order to refine our knowledge of its magnetic field strength and geometry, rotational period and spectral properties and variability. In this paper we report new Echelle SpectroPolarimetric Device for the Observation of Stars (ESPaDOnS) spectropolarimetric observations of HD 57682, which are combined with previously published ESPaDOnS data and archival Hα spectroscopy. This data set is used to determine the rotational period (63.5708 ± 0.0057 d), refine the longitudinal magnetic field variation and magnetic geometry (dipole surface field strength of 880 ± 50 G and magnetic obliquity of 79° ± 4° as measured from the magnetic longitudinal field variations, assuming an inclination of 60°) and examine the phase variation of various lines. In particular, we demonstrate that the Hα equivalent width undergoes a double-wave variation during a single rotation of the star, consistent with the derived magnetic geometry. We group the variable lines into two classes: those that, like Hα, exhibit non-sinusoidal variability, often with multiple maxima during the rotation cycle, and those that vary essentially sinusoidally. Based on our modelling of the Hα emission, we show that the variability is consistent with emission being generated from an optically thick, flattened distribution of magnetically confined plasma that is roughly distributed about the magnetic equator. Finally, we discuss our findings in the magnetospheric framework proposed in our earlier study.