This dataset contains the results presented in "No evidence that the majority of black holes in binaries have zero spin". In this paper, we systematically explored the effective and component spin distributions of binary black holes among the LIGO/Virgo GWTC-3 catalog. In particular, we tried to answer the following core questions, which have been the subject of active exploration and some debate in the literature: 1. Is there an excess of binary black holes with vanishing spin, as predicted by some theories of angular momentum transport in stellar cores? We find no evidence for an excess of vanishing spin systems. This finding is confirmed by three complementary analyses: one relying only on the Bayes factors between spinning and non-spinning priors for each BBH observation, one that seeks to model the distribution of effective aligned spins, and one modeling the distribution of component spin magnitudes and misalignment angles. Instead, we find BBH spin magnitudes to be consistent with a single, continuous distribution that remains finite at magnitude zero. 2. Do there exist binaries with component spins misaligned by more than 90 degrees relative to their orbits? We find a strong preference for the existence of such strongly misaligned spins. Our analysis of the BBH component spin distribution indicates that at least some component spins are misaligned from their orbits by more than 90 degrees. This result is robust under a variety of modeling choices regarding both the distribution of component spin magnitudes and tilts. The code used to generate this data can be found in the repository https://github.com/tcallister/gwtc3-spin-studies/. This repository includes jupyter notebooks that can be used to open, explore, and plot the files contained in this data set. Additional information about reproducing and/or using this dataset can be found in our associated documentation. Further notes: The files sampleDict_FAR_1_in_1_yr.pickle and injectionDict_FAR_1_in_1.pickle, used as inputs to our analyses, are created via code in the repository https://github.com/tcallister/get-lvk-data (see also https://zenodo.org/record/6505409). The file posteriors_gaussian_spin_samples_FAR_1_in_1.json, used for figure generation, was published by the LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration in support of the paper "The population of merging compact binaries inferred using gravitational waves through GWTC-3" (see https://zenodo.org/record/5655785).