USGS DEMs have published accuracy statements. Visit http://rockyweb.cr.usgs.gov/nmpstds/demstds.html for links to the National Map Accuracy Standards document and review the documentation in Part 2.
There is no general rule because, as the USGS states, the vertical accuracy depends on how the DEM was processed.
There is no general, well-founded rule for basing contour intervals on the DEM accuracy, because usually the contours serve multiple purposes. DEMs that have poor absolute vertical accuracy may very well have excellent relative accuracy among the contours and be able to support very detailed contours; indeed, they may need closely-spaced contours to reveal the information they contain.