Has anyone run into problems with a secondary antibody binding non-specifically to the tissue?

I am using a mouse monoclonal primary with a standard Vector Elite anti-mouse secondary, following antigen unmasking, followed by ABC and DAB as usual. The tissues are human tumors.  A couple of them are showing strong staining in many areas where there should be no staining.  Omitting the primary antibody makes no difference. Omitting both antibodies and using just the ABC complex results in a clean slide, so endogenous biotin is not the problem.  Apparently the secondary antibody is binding non-specifically to the tumor.  Has anyone else run into such a problem?  How did you address it?
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