Power efficiency and reliability are two issues facing digital signal processing (DSP) systems designed using CMOS and nanoscale process technologies. Power saving techniques like voltage overscaling (VOS) in CMOS technologies and the reliability issues in nanoscale processes make these systems susceptible to transient errors. These errors often manifest themselves as large magnitude errors at the application level and can severely degrade system performance. In this work we investigate the performance of recursive least squares (RLS) estimation under stochastic errors. The time recursive nature of the RLS technique can cause severe degradation of system performance under certain error conditions. An error detection mechanism based on observing weight updates can provide substantial system level performance improvements.