(Normally we would just consult the Census Web site for metadata, but it's down for an undetermined time...)
Census features derive from the TIGER files developed over the last 20 to 30 years. These files were assembled from multiple data sources, primarily the USGS 1:100,000 Digital Line Graphs and 1:24,000 USGS quadrangles. The accuracy of these data was improved systematically during the last 5-10 years, culminating in a recent test against GPS-derived "ground truth points":
The test verified that the spatial accuracy of the street network met the Census Bureau's horizontal spatial accuracy standard of CE95 at 7.6 meters (about twenty-five feet) or better. This accuracy standard requires that 95 percent of the time, the distance between the sample control points coordinates and their corresponding street centerline file intersection points not exceed 7.6 meters, i.e., a file point will fall within a radius of 7.6 meters of its corresponding control point.
It helps to recognize that these are tests of absolute positional accuracy. Relative inaccuracy would be reflected in distortions of true shapes and ought to be much, much better than 25 feet--but as far as I know, tests of such localized distortion (such as at the block level) have not bee reported.
Notice that scale is related to accuracy through its effect on precision: the larger the scale, the greater the precision and the more stringent are the accuracy requirements (as spelled out in the National Map Accuracy Standards, which roughly indicate that maps are expected to be accurate at most locations to within 1/2 to 1 millimeter on the map. At 1:100,000 scale, 1/2 mm = 100000*1/2 mm = 50 meters on the ground and at 1:24,000 scale, 1/2 mm represents 12 meters.) "Resolution" is an irrelevant concept, because the vector-based representations of these data consist of (lat, lon) coordinates in double precision, which has more enough precision to locate the nuclei of individual atoms.
We can nevertheless estimate some reasonable bounds on resolution from this information. For instance, representing Census blocks as an image with 20m pixels would introduce more imprecision into the shapes than is inherent in them, given the 7.6 m absolute accuracy: one can safely render blocks with sub-7.6 m pixels. Indeed, there is a risk of losing some of the smallest blocks altogether at a 20 m resolution. How much more resolution might be worthwhile to use will depend on the application and whether absolute positional accuracy or just relatively accurate rendering of the block shapes is needed. It also depends on what additional geographic data sources might be overlaid or combined with the blocks: it would make little sense--and be computationally wasteful--to use a resolution that is substantially finer than the accuracy inherent in the lowest-quality data source.