We present narrow-band CCD images of the HH 111 optical jet complex obtained at the ESO 3.5 m New Technology Telescope under conditions of excellent (less-than-or-equal-to 0."8 FWHM) seeing. These new images reveal the existence of a faint counterjet in the redshifted lobe of this bipolar outflow. We also identify the knot at the tip of the main jet as a further bow shock, in addition to the three already known in this system. By performing a partial deconvolution of the seeing profile, we have been able to resolve the knots in the trunk of the jet, which are found to have widths of about O."8, lengths of 0."8-1."1, and separation-to-width ratios of 2-4. The first bright knot at the base of the jet is split in two, perpendicular to the jet. We suggest that this structure is a ring of enhanced emission, viewed edge-on, such as might result from the passage of a puff of enhanced density through an oblique shock in the jet. We believe that more powerful (recurrent) eruptive events, possibly related to FU Orionis-type activity, are responsible for the main bow shocks. The core of knot V, the working surface which terminates the approaching lobe, is clearly divided into two zones of distinct excitation; a leading H-alpha strong zone and a trailing [S II] strong zone. We interpret these as the bow shock and Mach disk shock, respectively. In the wings of the bow shock, the [S II] emission is found to peak slightly closer to the source than does H-alpha, suggesting that we have resolved the spatially extended recombination region behind this oblique, hence weak, shock. We have been able to measure proper motions for the various knots in the HH 111 system by using our new images in conjunction with the original discovery images. When combined with existing radial velocity measurements these imply velocities away from the source of 320 km s-1 for the jet, 400 km s-1 for the approaching bow shock (V), and an average of 600 km s-1 for bow shocks X and Y in the receding lobe. The outflow lies at an angle of about 10-degrees to the plane of the sky, and the dynamical age of the complex is 800 yr.