Proper timing of gene expression requires that transcription factors (TFs) efficiently locate and bind their target sites within a genome. Theoretical studies have long proposed that one-dimensional sliding along DNA while simultaneously reading its sequence can accelerate TF's location of target sites. Sliding by prokaryotic and eukaryotic TFs were subsequently observed. More recent theoretical investigations have argued that simultaneous reading and sliding is not possible for TFs without their possessing at least two DNA-binding modes. The tumor suppressor p53 has been shown to slide on DNA, and recent experiments have offered structural and single molecule support for a two-mode model for the protein. If the model is applicable to p53, then the requirement that TFs be able to read while sliding implies that noncognate sites will affect p53's mobility on DNA, which will thus be generally sequence-dependent. Here, we confirm this prediction with single-molecule microscopy measurements of p53's local diffusivity on noncognate DNA. We show how a two-mode model accurately predicts the variation in local diffusivity, while a single-mode model does not. We further determine that the best model of sequence-specific binding energy includes terms for "hemi-specific" binding, with one dimer of tetrameric p53 binding specifically to a half-site and the other binding nonspecifically to noncognate DNA. Our work provides evidence that the recognition by p53 of its targets and the timing thereof can depend on its noncognate binding properties and its ability to change between multiple modes of binding, in addition to the much better-studied effects of cognate-site binding.