Aims: One of the most striking features predicted by standard models of galaxy formation is the presence of anti-correlations in the matter distribution on large enough scales (r > r_c). Simple arguments show that the location of the length scale r_c, marking the transition from positive to negative correlations, is the same for any class of objects as for the full matter distribution; i.e. it is invariant under biasing. This scale is predicted by models to be at about the same distance of the scale signaling the baryonic acoustic oscillation scale rbao. Methods: We test these predictions in the newest SDSS galaxy samples where it is possible to measure correlations on ~100 Mpc/h scales both in the main galaxy (MG) and in the luminous red galaxy (LRG) volume-limited samples. We determine, by using three different estimators, the redshift-space galaxy two-point correlation function. Results: We find that, in several MG samples, the correlation function remains positive on scales >250 Mpc/h, while it should be negative beyond rc ≈ 120 Mpc/h in the concordance LCDM. In other samples, the correlation function becomes negative on scales <50 Mpc/h. To investigate the origin of these differences, we considered in detail the propagation of errors on the sample density into the estimation of the correlation function. We conclude that these are important at large enough separations and that they are responsible for the observed differences between different estimators and for the measured sample-to-sample variations in the correlation function. We show that in the LRG sample the scale corresponding to rbao cannot be detected because fluctuations in the density fields are too large in amplitude. Previous measurements in similar samples have underestimated volume-dependent systematic effects. Conclusions: We conclude that, in the newest SDSS samples, the large-scale behavior of the galaxy correlation function is affected by intrinsic errors and volume-dependent systematic effects that make the detection of correlations only an estimate of a lower limit of their amplitude, spatial extension, and statistical errors. We point out that these results represent an important challenge to LCDM models as they largely differ from its predictions.