We present the results of a multiepoch Very Long Baseline Array study of the powerful radio source 4C +12.50 (PKS 1345+125) at a wavelength of 2 cm. This compact radio source is associated with a hidden quasar whose host galaxy shows signs of a recent merger. It has been classified as a compact symmetric source (CSO) as a result of its small overall size (~220 pc) and twin-jet morphology, although it also has faint extended emission that may be a relic of previous activity. We report the detection of exceedingly high linear fractional polarization in isolated features of the southern jet (up to 60%), which is highly unusual for a CSO. Given the large amount of gas present in the host galaxy, we would expect significant Faraday depolarization across the whole source, unless the depolarizing gas is fairly clumpy. The southern jet also contains two features that are moving outward from the core at apparent speeds of v/c = 1.0 ± 0.3 and 1.2 ± 0.3. These represent the first positive detections of superluminal motion in a CSO and, taken together with the jet-to-counterjet flux ratio, suggest an intrinsic flow speed of v/c = 0.84 ± 0.12. The apparent ridgeline of the jet and counterjet is consistent with a conical helix of wavelength 280 pc that is the result of Kelvin-Helmholtz instabilities driven by a slow precession of the jet nozzle. A fit to the data implies that the nozzle is precessing around a cone with half-angle 23°, whose axis lies at an angle of 82° to the line of sight. We suggest that the S-shaped jet morphologies commonly seen in recent active galactic nucleus outflows such as 4C +12.50 may simply reflect the fact that their black hole spin axes are still precessing and have not had sufficient time to align with their accretion disks.