We have obtained narrowband images and high-resolution spectra of the planetary nebulae NGC 6337, He 2-186, and K4-47 with the aim of investigating the relation between their main morphological components and several low-ionization features present in these nebulae. The data suggest that NGC 6337 is a bipolar PN seen almost pole-on, with polar velocities of >=200 km s-1. The bright inner ring of the nebula is interpreted to be the ``equatorial'' density enhancement. It contains a number of low-ionization knots and outward tails that we ascribe to dynamical instabilities leading to fragmentation of the ring or transient density enhancements due to the interaction of the ionization front with previous density fluctuations in the interstellar medium. The lobes show a pronounced point-symmetric morphology and two peculiar low-ionization filaments, the nature of which remains unclear. The most notable characteristic of He 2-186 is the presence of two high-velocity (>=135 km s-1) knots from which an S-shaped lane of emission departs toward the central star. K4-47 is composed of a compact core and two high-velocity, low-ionization blobs. We interpret the substantial broadening of line emission from the blobs as a signature of bow shocks, and using the modeling of Hartigan, Raymond, & Hartman, we derive a shock velocity of ~150 km s-1 and a mild inclination of the outflow on the plane of the sky. We discuss possible scenarios for the formation of these nebulae and their low-ionization features. In particular, the morphology of K4-47 hardly fits into any of the usually adopted mass-loss geometries for single asymptotic giant branch stars. Finally, we discuss the possibility that point-symmetric morphologies in the lobes of NGC 6337 and the knots of He 2-186 are the result of precessing outflows from the central stars. Based on observations obtained at the 3.5 m New Technology Telescope (NTT) of the European Southern Observatory, and at the 2.6 m Nordic Optical Telescope (NOT) operated on the island of La Palma by NOTSA, in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofísica de Canarias, and with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA for NASA under contract NAS5-26555.