The Deep Space Network (DSN) Radio Reference Frame consists of a catalog of angular positions for 281 extragalactic radio sources based on VLBI measurements made during the period from 1978 to 1992. A realistic assessment of the accuracy of these source position estimates must consider both modeled stochastic errors and systematic model deficiencies. Modeled stochastic errors include thermal noise (signal-to-noise ratio) and fluctuations in tropospheric refractivity due to the changing distribution of water vapor. These modeled errors result in a median formal position uncertainty of ≈0.3 milliarcseconds (mas). In particular, we examine the effect of changing the model for inter-observation correlations of water vapor fluctuations on estimated parameters. Next, a comparison of our radio source positions with independently determined positions is presented as evidence of systematic errors at ≤ 0.5 mas. We discuss several aspects of VLBI model accuracy focussing on tidal effects, antenna thermal expansion, pressure loading, source structure, precession and nutation. Prospects for reducing these errors are also discussed. We conclude by combining these estimates of modeled stochastic errors and systematic errors into an overall assessment of < 1.0 mas for the current accuracy of the DSN extragalactic radio frame.