Asteroid observations by the WISE space telescope and the analysis of those observations by the NEOWISE project have provided more information about the diameter, albedo, and other properties of approximately 164,000 asteroids, more than all other sources combined. The raw data set from this mission will likely be the largest and most important such data on asteroids available for many years. To put this trove of data to productive use, we must understand its strengths and weaknesses, and we need clear and reproducible methods for analyzing the data set. This study critically examines the WISE observational data and the NEOWISE results published in both the original papers and the NASA Planetary Data System (PDS). There seem to be multiple areas where the analysis might benefit from improvement or independent verification. The NEOWISE results were obtained by the application of 10 different modeling methods, many of which are not adequately explained or even defined, to 12 different combinations of WISE band data. More than half of NEOWISE results are based on a single band of data. The majority of curve fits to the data in the NEOWISE results are of poor quality, frequently missing most or all of the data points on which they are based. Complete misses occur for about 30% of single-band results, and among the results derived from the most common multiple-band combinations, about 43% miss all data points in at least one band. The NEOWISE data analysis relies on assumptions that are in many cases inconsistent with each other. A substantial fraction of WISE data was systematically excluded from the NEOWISE analysis. Building on methods developed by Hanuš et al. (2015), I show that error estimates for the WISE observational data were not well characterized, and all observations have true uncertainty at least a factor of 1.3–2.5 times larger than previously described, depending on the band. I also show that the error distribution is not well fit by a normal distribution. These findings are important because the Monte Carlo error-analysis method used by the NEOWISE project depends on both the observational errors and the normal distribution. An empirical comparison of published NEOWISE diameters to those in the literature that were estimated by using radar, occultation, or spacecraft (ROS) measurements shows that, for 129 results involving 105 asteroids, the NEOWISE diameters presented in tables of thermal-modeling results exactly match prior ROS results from the literature. While these are only a tiny fraction (0.06%) of the asteroids analyzed, they are important because they represent the only independent check on NEOWISE diameter accuracy. After removing the exact matches and adding additional ROS results, I find that the accuracy of diameter estimates for NEOWISE results depends strongly on the choice of data bands and on which of the 10 models was used. I show that systematic errors in the diameter estimates are much larger than previously described and range from − 5% to + 23%. In addition, random errors range from − 15% to + 19% when all four WISE bands were used, and from − 39% to + 57% in cases employing only the W2 band. The empirical results presented here show that much work remains to be done in analyzing data from the WISE/NEOWISE mission and interpreting it for asteroid science.