Since PCR products, that were obtained using combination of our own reagents (Taq.pol from New England Biolabs, MgCl2 from NCB and so on), were faint on gel I decided to use Qiagen PCR amplification kit, which I found in the freezer. I run two reactions at the same. As the result bands for PCR products from Qiagen were more visible and stronger.
Conclusion: use Qiagen reagent kit for further PCR amplifications
Problem: still having multiple bands and smears