I guess the non-specific bands might be because of the primer dimer formation or magnifying something else in your sample rather than your target DNA which might have resulted because your DNA is not separated well. So, use DMSO, it might work as Lakshmi Sirisha has suggested in the above message. Also try doing HOT-START PCR. 95 degree centigrade for 10 minutes, stop the reaction or set the setting so that reaction will stop at that point and then add the TAG DNA polymerase. I think that might work well.