“Paul was wrong about a lot of things so we don’t have to go by what he said.”

No

Peter, the one chosen by Jesus to be the lead apostle had this to say about Paul’s writings:

Bear in mind that our Lord’s patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction. 2 Peter 3;16,17

Peter calls Paul “our dear brother”, said that Paul wrote “with the wisdom that God gave him”.  He refers to Paul’s writings as “Scriptures,” saying that those who distort them are “ignorant and unstable people” who are headed for destruction by doing so.

Some protest that Peter’s “opinion” isn’t a good example because he was “always saying the wrong thing.”  The Bible is unique in not hiding people’s miss-steps, even sins.  However, none of the inappropriate things that Peter said (Matthew 16;22,23; 17:4) were for our instruction but only his reactions to the utterly new things he heard and saw. Even if Peter had instructed the wrong thing, that would give us no reason to doubt Paul.

Of course, Jesus is the better witness:

But the Lord said to Ananias, “Go! This man is my chosen instrument to proclaim my name to the Gentiles and their kings and to the people of Israel. Acts 9:15

Jesus sought Saul of Tarsus/Paul out and appeared to him personally to call him to be his follower.  Jesus chose Paul to proclaim his name to us so we pick and choose what we observe of Paul’s teachings* at peril of rejecting Jesus’ commands.

*Perhaps a few things are only for their culture but probably not as many as people think—and everyone seems to have differing opinions on this.

“It’s acceptable for Christians to be in the military because Jesus never told the centurions to stop what they were doing.”

No


When Jesus heard this, he was amazed and said to those following him, “Truly I tell you, I have not found anyone in Israel with such great faith. I say to you that many will come from the east and the west, and will take their places at the feast with Abraham, Isaac and Jacob in the kingdom of heaven. But the subjects of the kingdom will be thrown outside, into the darkness, where there will be weeping and gnashing of teeth.”

Then Jesus said to the centurion, “Go! Let it be done just as you believed it would.” And his servant was healed at that moment. Matthew 8:10-13

Jesus commended one centurion for his faith—not his occupation. Jesus also never told the “woman at the well” that she was wrong for having five husbands—and divorces, as well as living with a man who was not her husband. Neither is there any record of Jesus directly telling prostitutes that they were in the wrong profession but that doesn’t mean he commended it.  Each of these things are covered in his teachings, which he clearly had in mind for his followers to obey, whether he made a direct, personal application to them individually or not.

Jesus taught:
“Love your enemy.” Matthew 5:43-48

“Bless those who curse you.” Luke 6:28

“You have heard that it was said, ‘Eye for eye, and tooth for tooth.’ But I tell you, do not resist an evil person. If anyone slaps you on the right cheek, turn to them the other cheek also.” Matthew 5:38-40

“My kingdom is not of this world. If it were, my servants would fight to prevent my arrest by the Jewish leaders. But now my kingdom is from another place.” John 18:36

Peter said, “Do not repay evil with evil or insult with insult. On the contrary, repay evil with blessing, because to this you were called so that you may inherit a blessing.” 1 Peter 3:9

Paul said, 
“Do not be overcome by evil, but overcome evil with good.” Romans 12:21

“For though we live in the world, we do not wage war as the world does. The weapons we fight with are not the weapons of the world.” 2 Corinthians 10:3, 4

“For our struggle is not against flesh and blood, but against the rulers, against the authorities, against the powers of this dark world and against the spiritual forces of evil in the heavenly realms.” Ephesians 6:12

Jesus’ expects his followers to be different because they’re not operating the way this world does, but in God’s way.  By not telling the centurion—just one man, that he shouldn’t be in the military, Jesus did not wipe out all of his teachings about loving ones enemy.

“If you hold to my teaching, you are really my disciples. Then you will know the truth, and the truth will set you free.” John 8:31,32

"Whoever has my commands and keeps them is the one who loves me. The one who loves me will be loved by my Father, and I too will love them and show myself to them.” John 14:21

Jesus replied, “Anyone who loves me will obey my teaching. My Father will love them, and we will come to them and make our home with them. Anyone who does not love me will not obey my teaching. These words you hear are not my own; they belong to the Father who sent me.” 
John 14:23,24