Aims. Our aim is to investigate the nature of the X-Ray Flash (XRF) of August 24, 2005. Methods. We present comprehensive photometric R-band observations of the fading optical afterglow of XRF 050824, from 11 min to 104 days after the burst. In addition we present observations taken during the first day in the BRIK bands and two epochs of spectroscopy. We also analyse available X-ray data. Results. The R-band lightcurve of the afterglow resembles the lightcurves of long duration Gamma-Ray Bursts (GRBs), i.e., a power-law, albeit with a rather shallow slope of α = 0.6 (Fv ∝ t -α). Our late R-band images reveal the host galaxy. The rest-frame B-band luminosity is ∼0.5 L*. The star-formation rate as determined from the [OII] emission line is ∼1.8 M⊙ yr -1. When accounting for the host contribution, the slope is α = 0.65 ± 0.01 and a break in the lightcurve is suggested. A potential lightcurve bump at 2 weeks can be interpreted as a supernova only if this is a supernova with a fast rise and a fast decay. However, the overall fit still shows excess scatter in the lightcurve in the form of wiggles and bumps. The flat lightcurves in the optical and X-rays could be explained by a continuous energy injection scenario, with an on-axis viewing angle and a wide jet opening angle (θj ≳ 10°). If the energy injections are episodic this could potentially help explain the bumps and wiggles. Spectroscopy of the afterglow gives a redshift of z = 0.828 ± 0.005 from both absorption and emission lines. The spectral energy distribution (SED) of the afterglow has a power-law (Fv ∝ v-β) shape with slope β = 0.56 ± 0.04. This can be compared to the X-ray spectral index which is βX = 1.0 ± 0.1. The curvature of the SED constrains the dust reddening towards the burst to Av < 0.5 mag.