This is really the nature of the beast. PDF is a rendered format, so is MOBI. Converting from one rendered format to another is going to introduce these imperfections.
As I see it, you have two options: 1)convert the PDF to MS WORD (and fix all the formatting errors), then run it through Calibre and 2)read it only in a PDF reader on a mobile device.
Actually there is another option: use Amazon's Personal Docs/Content server (which will convert automatically from PDF to its mobi format). https://www.amazon.com/gp/help/customer/display.html/ref=hp_pdoc_main_short_us?nodeId=200767340 I have no idea whether Amazon's conversions are any better than Calibre; probably not, but it's worth a shot.
MS Word poses other conversion challenges, but at least it's something which can be processed more easily than PDF.