“How do I break through to the spiritual conversation when someone I am trying to witness to tries to constantly bring up ‘errors’ or ‘mistakes’ in the Bible, such as ‘Joshua speaking to the sun to stand still rather than the earth to stop moving,’ or differences in the gospels such as ‘One gospel says there was more than one man in chains in the cave possessed with legions of demons and another gospel says there was one man possessed with legions of demons?’”
The human mind is in a place of contention against God and His Law (see Romans 8:7). If you answer these questions, no doubt he will come back with more than he has collected from Internet sites. All he wants to do is fortify his godless worldview so that he can indulge in his beloved sins.
So what you should do is address his conscience. Take him through the Ten Commandments as Jesus did in Mark 10:17, or as Paul did in Romans 2:18-20. This will have the effect of stopping his mouth (see Romans 3:19-20). To see how this is done, watch www.evolutionVsGod.com