With its bright and wide equatorial waist seen almost edge-on (`the butterfly body') and the faint and broad bipolar extensions (`the butterfly wings'), NGC 650-1 is the archetypical example of bipolar planetary nebula (PN) with butterfly morphology. We present here deep high-resolution broad- and narrow-band optical images that expose the rich and intricate fine structure of this bipolar PN, with small-scale bubble-like features and collimated outflows. A SHAPE spatio-kinematic model indicates that NGC 650-1 has a broad central torus with an inclination angle of 75° with respect to the line of sight, whereas that of the bipolar lobes, which are clearly seen in the position-velocity maps, is 85°. Large field of view deep images show, for first time, an arc-like diffuse envelope in low- and high-excitation emission lines located up to 180 arcsec towards the east-south-east of the central star, well outside the main nebula. This morphological component is confirmed by Spitzer MIPS and WISE infrared imaging, as well as by long-slit low- and high-dispersion optical spectroscopic observations. Hubble Space Telescope images of NGC 650-1 obtained at two different epochs ˜14 yr apart reveal the proper motion of the central star along this direction. We propose that this motion of the star through the interstellar medium compresses the remnant material of a slow asymptotic giant branch wind, producing this bow-shock-like feature.