We analyze the fluctuations in the correlation exponents obtained for noncoding DNA sequences. We find prominent sample-to-sample variations as well as variations within a single sample in the scaling exponent. To determine if these fluctuations may result from finite system size, we generate correlated random sequences of comparable length and study the fluctuations in this control system. We find that the DNA exponent fluctuations are consistent with those obtained from the control sequences having long-range power-law correlations. Finally, we compare our exponents for the DNA sequences with the exponents obtained from power-spectrum analysis and correlation-function techniques, and demonstrate that the original "DNA-walk" method is intrinsically more accurate due to reduced noise.