The fundamental plane (FP) is fitted to over 400 early-type galaxies in 20 nearby clusters with km s 1 cz ∼ 4000–11,000 using our photometry and spectroscopy, in addition to measurements culled from the literature. We find that a significant gap exists in the observed distribution of the rms scatter, , S separating the clusters that fit well from those that do not. This gap occurs at the global FP scatter and is found to be ASS inconsistent at the 99% level, with the hypothesis that the clusters have been drawn from a single underlying distribution. This appears to have consequences for the measured cluster peculiar velocities (PVs). While the mean PVs of the two subsamples defined by are zero within their errors, the 9 highASS clusters exhibit much higher PV scatter than the 11 lowS S clusters. Assuming early-type galaxies in clusters are drawn from a single population, there should be no correlation between PV scatter and . However, the significance of the inS crease in PV scatter above is 99%. Our results imply that ASS the presence of error unaccounted for in the PV measurements of the highclusters may make them unsuitable for peculiar S motion studies. A thorough list of tests demonstrates that this result does not appear to arise from problems with the observations or an oversight made during our analysis. Instead, the highclusters S tend to have a problematic combination of intrinsic global properties indicative of the presence of substructure, which Bothun et al. (1990, ApJ, 353, 344) point out could lead to biased PV measurements. The strongest evidence comes from X-ray measurements that indicate the degree of virialization within the clusters. We find that the clusters with X-ray luminosities greater than 10 ergs s , as determined with data from the Einstein Observatory and ROSAT, all fit the FP well and have small PV. In addition, the clusters with high early-type galaxy fractions and high velocity dispersions tend to have low . S Conversely, significant substructure known to exist in clusters such as A400, A2634, and A2151 could contribute to the large . This evidence suggests that all-sky surveys that mix together S both classes of clusters, as characterized by , may artificially S inject signal into the observed PV field. Ultimately, we expect that a carefully chosen sample of clusters based on high X-ray luminosity and low might result in a refined FP distance S indicator. This may also alleviate the current discord between PV surveys, some of which report bulk motions of 700 km s 1 on scales of 150 Mpc. These measurements are not only discrepant, but such large flow amplitudes cannot be accommodated by any present cosmological model that assumes the average random motion of clusters superimposed on the Hubble flow is driven by gravity and the underlying mass distribution (e.g., Strauss et al. 1995, ApJ, 444, 507). Therefore, if accurate, such results would seriously strain models, which would have to simultaneously explain them and reconcile them with other opposing measurements of the cosmic microwave background (CMB), Type Ia supernovae, the evolution of the cluster abundance, and peculiar velocities made using other methods. We therefore test evidence that clusters within redshift depths of 10,000 km s 1 are streaming coherently and at high velocity with respect to the inertial frame defined by the velocity dipole of the CMB. We find that when we add to the cluster motions any one of the large bulk flows measured by Lauer & Postman (1994, ApJ, 425, 418), Hudson et al. (1999, ApJ, 512, L79), or Willick (1999, ApJ, 522, 647), the PV scatter is higher than in the CMB frame. In addition, the lowset excludes the S Lauer & Postman and Willick frames as the natural rest frame of the universe and disagrees with the Hudson et al. result at the 97% level. Indeed, the data show no other evidence of a large coherent flow and are consistent with the majority of other PV studies. Finally, when the filter is applied to our sample, a relatively S quiescent Hubble flow is revealed. If the lowclusters, which S include the most massive, better trace the underlying mass distribution, the one-dimensional rms peculiar velocity is limited to 250 km s 1 with 90% confidence. This amount of random motion implies , a value agreeing with nearly 0.6 Q j ! 0.43 0 8 all recent measurements made via independent methods, further suggesting that more reliable peculiar velocity results will be obtained using the most massive and relaxed clusters.