If playing with temperature doesn't work, you can try nested PCR. Choose a set of primers upstream and downstream of your target primers, making sure these are unique in the genome and don't form hairpins. This would create a PCR product larger than your target gene, but would include your target gene. PCR out that larger product and then use that product as a template for your actual PCR with your current primers. That should get rid of any contaminating bands.
Try adding DMSO at a concentration of 10% or if it doesn't work..
Prepare your reaction mix without enzyme,,, boil the reaction mix (containing template and primers but not enzyme) at 100 degree for 3-5 min...and cool slowly in the waterbath,,,(heat turned off)..till it comes to 30-40 degree. Add the enzyme to reaction mix...start the reaction with extension step at 72 degree for 1 min followed by normal PCR cycles starting from denaturation...
Hope it works for you...if you are not getting the expected band
If you are getting the expected band and in addition to that you are getting non specific bands then add glycerol at 10% to your reaction mix...it works good to get rid of non specific bands....
To optimise PCR, you can 1) try dilution series of template, 2) annealing temperature series, 3) avoid excessive elongation times. Diluting the template is by far the simplest and often most rewarding strategies, most people use too much template anyway. However, primers are cheap and quick to order, one should never spend too much time optimising, the more you try things out, the higher the risk that your lab, your solutions, and your pipettes are contaminated with the wrong amplification products. Once these products have been made, they are perfect templates for future PCRs with that particular primer pair, and thus very dangerous contaminants. Willingness to evaluate the suitability of your current primers and being prepared to design better primers and order them is an important attribute to the successful PCR operator. The worst thing that can happen to a primer is to have a 4 bp palindrome at the 3'end, or longer. This must be avoided at all cost, and when you have to amplify in a particular region to build a fusion protein, the only way out is to make the primers longer at the 3' end, even if it costs a bit more. Longer primers means higher specificity and higher annealing temperatures, so thats a win win win situation. Good luck with it. :)