First off why would you use SW inventory, it is useless.
https://www.enhansoft.com/blog/configuration-manager-and-software-inventory-proceed-with-caution
https://www.enhansoft.com/blog/how-do-you-determine-the-length-of-a-software-inventory-scan-cycle
https://www.enhansoft.com/blog/slow-software-inventory-cycle-in-sccm-2012
Secondly the log on your mp is mp_sinv.log for SW inv.
Thirdly, I would pick one problem and work only on it. IMO I would worry about your HW inv far more than SDW inv.