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A representative sample of 12 extended quasars from the 3CR catalog has been imaged at 4.9 GHz using the VLA. These full synthesis observations typically achieve an rms noise of 20 µJy per beam, at a resolution (FWHM) of 0.34" to 0.38". Jets are detected on at least one side of every source. The jets are well collimated compared with those in less powerful sources, but spreading is detected in most of them. The opening angles of several jets are not constant, but show recollimation after an initial regime of rapid spreading. Many of the jets contain quasiperiodic strings of knots, of which the knot closest to the central feature is usually the brightest (until the jet nears its hot spot). The degrees of linear polarization at the jet knots range from < 5% to ~ 50%, but show no common trend with distance along the jets. In knots that are elongated in directions close to that of the jet, the E vectors tend to be orthogonal to the jet axis. The exceptions - misaligned knots with misaligned polarizations-tend to be bright features near large bends in the jets. Many of the jets are initially straight to within a few degrees, but bend more in the outer part of the source. The prominence of the inner, straighter jet segments relative to the extended lobes correlates significantly with the prominence of the milliarcsecond-scale central features, but the prominence of the more bent jet segments does not. Candidates for counterjet emission are detected in seven sources, but there is no unambiguous, continuous counterjet in any of them. Estimates of the flux density ratios between the straighter jet segments and the counterjets based on these tentative detections range from 1.2:1 to > 175:1. There is no evidence in this sample that counterjet detectability correlates with such putative inclination indicators as central feature prominence or projected linear size. There is also no evidence that the prominence of the counterjets anticorrelates with that of the jets as predicted by simple relativistic-beaming models for the jet/counterjet asymmetry. There is, however, strong evidence that large bends in the main jet favor counterjet detection, and there are no counterjet candidates opposite long, uninterrupted straight segments of the main jets. The detectability of the counterjets in these quasars may therefore be strongly influenced by interactions between the underlying beams and inhomogeneities in the surrounding material. We offer a new empirical definition of the term "hot spot" that is intended to improve the distinction between such features and "jet knots." Both the compactness of hot spots and their position in the lobe are affected by whether they are fed by a detectable jet. When the hot spots differ significantly in compactness, the more compact one is always on the jetted side. Jetted hot spots are also more likely to be recessed deeply from the outer edge of their lobes than are their counterjetted counterparts. The jetted hot spot is less prominent relative to other extended emission if the jet bends through a large angle, particularly if a large bend occurs abruptly. The counterjetted hot spot is also less well defined if the jet is more bent. The lobes of several sources show considerable inhomogeneity, including filamentation. There is little difference in the inhomogeneity of the jetted and counterjetted lobes if the hot spots are excluded. The lobes have a common linear polarization pattern, with low polarization at the center and high polarization (often reaching 40% to 60%) near the edges. This pattern matches the expectations of models in which the magnetic field in the lobes is provided by passively expanding the field in the jets. The lobes in sources with promising counterjet candidates are often S-symmetric relative to the jet axis and their hot spots are more misaligned than in sources without such candidates. Counterjets may therefore be easier to detect if the jets change orientation during the lifetime of the source. We outline the implications of our results for various models of the prominence and asymmetries of central features, jets, counterjets, and hot spots. The correlations between the prominence and sidedness of the large-scale straight jet segments and of the small-scale central features favor models in which the kiloparsec-scale jets initially have bulk relativistic velocities. The slope of the prominence correlation is less than expected if the larger-scale jets have characteristic Lorentz factors as high as those in the milliarcsecond-scale features, however. This result is fragile within our small sample, but other aspects of our data also suggest that another phenomenon, closely coupled to jet bending, helps to determine the prominence of features far from the central region. Overall, our data favor "tired jet" models in which the average jet velocity decreases with increasing distance from the central object. This makes it harder for the simplest relativistic-jet models to account for the systematic differences in compactness and placement of jetted and counterjetted hot spots. The models may need refinement to include a range of Lorentz factors in the jets at any given distance from the quasar.