1.     Jesus' lineage was traced through David's son Solomon. Mt.1:6.
Jesus' lineage was traced through David's son Nathan. Lk.3:31.

This is something that I have seen multiple explanations for, none of which have proven satisfactory to me.  I am willing to grant that this is at least an apparent contradiction.

1. The announcement of the special birth came before conception. Lk.1:26-31.
   The announcement of the special birth came after conception. Mt.1:18-21.

There is no contradiction in this.  In Luke, Mary is told that she would become pregnant prior to her pregnancy.  In Matthew, Joseph is told that Mary’s pregnancy is from God to address his concerns.  This is only a contradiction if one contends that only a single event is being recorded with a shifting of some details.  But there is little overlap of detail, and the purpose for the two is quite different.

1. Jesus' parents were told of their son's future greatness. Mt.1:18-21; Lk.1:28-35.
   Jesus' parents knew nothing of their son's potential. Lk.2:48-50.

The first of these is a proclamation by an angel to Joseph (in Matthew) and Mary (Luke 1:28-30) concerning who the child would be and his parentage.  The Luke 2:48-50 passage concerns an event when Jesus is 12 years old and while it does imply that Mary and Joseph did not understand Jesus need to be in the temple, that falls far short of the claim here that they knew nothing of his potential.

1. The angel told Joseph. Mt.1:20.
   The angel told Mary. Lk.1:28.

Since when is it a contradiction to tell two different people something?  Matthew tells the birth of Jesus primarily from Joseph’s perspective while Luke does from Mary’s.  During the course of the narrative, each one is informed of the birth at the appropriate time. – see the response to #2

1. There were 28 generations from David to Jesus. Mt.1:17.
   There were 43 generations from David to Jesus. Lk.3:23-31.

This is related to #1 and is not a separate contradiction.  The genealogies are different.  !, 5 & 6 are all making the same claim.

1. Jacob was Joseph's father. Mt.1:16.
   Heli was Joseph's father. Lk.3:23.

See the response to #1 and #5 above.

1. He was to be called Emmanuel. Mt.1:23.
   He was called Jesus. Mt.1:25.

The name the child is to be given is Jesus.   Emmanuel, God with us, is what he will be called.  Emmanuel was not to be his name, anymore than ‘World’s Greatest Athlete’ is the name given to the winner of the Olympic decathlon; but it is what he is called.

1. Joseph, Mary, and Jesus flee to Egypt while Herod slaughters all males under 2 years old. Mt.2:13-16. (Note: Jesus' cousin, John, was also under 2 and survived without having to flee.)
   Joseph, Mary, and Jesus did not flee to Egypt, but remained for temple rituals. No slaughter of infants is mentioned! Lk.2:21-39.

John was not born anywhere near Bethlehem, which is the place mentioned in connection with the slaughter of the infants.  The temple rituals occur when Jesus is 8 and 40 days old.  There is plenty of time for that to occur and still be able to flee before hitting two years old.  There is little overlap in the birth stories between Matthew and Luke.  That one records an event that the other does not is by no means a contradiction.

1. Jesus was tempted during the 40 days in the wilderness. Mk.1:13.
   Jesus was tempted after the 40 days in the wilderness. Mt.4:2,3.

Marks account here is a two verse description of Jesus time in the wilderness following his baptism, giving little detail.  Matthew and Luke provide more details concerning 3 of the temptations.  The initial temptation presented in Matthew occurs after Jesus has fasted for 40 days and is hungry.  Could there have been more temptations preceding this?  I don’t see why not.  And the temptation to deal with his hunger makes more sense at the end of an extended fast.  Is this a contradiction?  Or is it the difference between a summary statement and a more detailed description?

1. The devil first took Jesus to the pinnacle, then to the mountain top. Mt.4:5-8.
   The devil first took Jesus to the mountain top, then to the pinnacle. Lk.4:5-9.

Yes they are in a different order.  Is the story any different because of it?  Does it matter?  Neither the author of Matthew or Luke appear to be eye witnesses or to have personally heard Jesus recounting of the experience.  Instead they are recording oral accounts that have the events in different orders.  Call it a contradiction if you will, but the story is the same in both accounts.

1. Satan tempted Jesus. Mt.4:1-10; Mk.1:13; Lk.4:1,2.
   Satan had no interest in Jesus. Jn.14:30.

Not sure how the phrase in John 14:30, “He (Satan) has no hold on me” is taken to mean that Satan has no interest in Jesus.  It means he has no control over him, not interest in him.  Two different things.

1. The baptism of Jesus was with the "Holy Ghost". Mk.1:8; Jn.1:33.
   Fire was also added to the baptism. Mt.3:11; Lu.3:16.

How does “He will baptize you with the Holy Spirit and with fire” contradict “He will baptize you with the Holy Spirit”.  Some accounts adding detail that other accounts omit does not make for a contradiction.  If they said or meant something different it would be a contradiction.  When one person says that he heard thunder all night and another says there was thunder and lightning all night, do the two statements contradict each other?

1. John knew of Jesus before he baptized him. Mt.3:11-13; Jn.1:28,29.
   John knew nothing of Jesus at all. Mt.11:1-3.

Matthew 3:11-13 indicates that John had some prior knowledge of the role that Jesus would fill, although no indication that he had any personal knowledge of him.

John 1:28-33 indicates that John had been given a sign to identify Jesus when he came, and that he had some prior knowledge of his role, although no indication he had any personal knowledge of him.

Matthew 11:13 records John (in prison at this time) sending some of his disciples to Jesus to find out for sure if he was the one John had been looking forward to, or if there was another coming.  This passage does not say that John knew nothing of Jesus.  It does say that while in prison he had begun to doubt that Jesus was really the one for whom he had been preparing the way.

There is nothing in these three passages that would begin to be a contradiction.

1. Jesus begins his ministry after John's arrest. Mk.1:13,14.
   Jesus begins his ministry before John's arrest. Jn.3:22-24.

The passage in John says that Jesus was in the Judean countryside preaching and baptizing, as was John.  Mark records that after John is put into prison, Jesus goes to Galilee.  I don’t see the contradiction in this.  Only if you assume that there was nothing happening between Mark 1:13 and 14 could this be a possible issue, and there is nothing to imply in this passage that they were tightly connected in time.

1. It is recorded that Jesus saw the spirit descending. Mt.3:16; Mk.1:10.
   It is recorded that John saw the spirit descending. Jn.1:32.

Indeed they say that.  Is it a contradiction if I say I watched a football game and someone else also claimed to have watched it?  Or is it a contradiction because all three sources referenced did not list everyone who saw the event?

1. The heavenly voice addressed the gathering. Mt.3:17.
   The heavenly voice addressed Jesus. Mk.1:11; Lk.3:22.

This is the same event as the preceding one.  Although I don’t know where it is expressed in the Matthew passage that the voice addressed the crowd.  All of these passages mention only Jesus in connection with the voice.  That does not rule out others hearing it, and in my opinion they likely did, but a contradiction?  I can’t see it.

1. Immediately after the baptism, Jesus spent 40 days in the wilderness. Mt.4:1,2; Mk.1:12,13.
   Three days after the baptism, Jesus was at the wedding in Cana. Jn.2:1.

Yes, they do present a different timeline, as the Gospels frequently do.  Ordering the events sequentially by time seemed not to be a priority for most of the gospel writers.

1. Jesus went to Bethphage and the Mt. of Olives, then left for Bethany. Mt.21:1,17.
   Jesus went to Bethphage and Bethany at the Mt. of Olives. Mk.11:1; Lk.19:29.
   Jesus went to Bethany and then Jerusalem. Jn.12:1,12.

Actually, Matthew says that Jesus went to Bethphage, then to Jerusalem and then back to Bethany to spend the night.  Bethany and Bethphage were two small villages to the east of Jerusalem with Bethphage being the nearer.  And Bethany is identified as being the home of Lazarus and his sisters.  So John has Jesus spending time in Bethany prior to the Passover.  He passes through Bethphage on the way to Jerusalem, picking up the donkey and then returns that night to Bethany.  The only possible contradiction I can see from this is that Mark and Luke ignore the time Jesus spent with Lazarus in Bethany and just say he went to the villages.  And omission of a detail like that is not, at least to my mind, a contradiction.

1. Jesus and his disciples taught in Capernaum. Mk.1:20,21.
   Only Jesus taught in Capernaum. Lk.4:30,31.

Again, a difference in the timeline, Luke records the driving out of the evil spirit prior to calling the disciples while Mark reverses the order.

1. Peter was chosen, with Andrew, by the Sea of Galilee. Mt.4:18-20; Mk.1:16-18.
   Peter was chosen, with James and John, by the lake of Gennesaret. Lk.5:2-11.
   Andrew chose Jesus and then got Peter to join. Jn.1:35-42.

The Matthew and Mark account record Jesus calling Peter and his brother Andrew along with James and his brother John to follow as his disciples, while Luke does indeed neglect mention of Andrew.  But the issue here is easily one of omitted detail.  Andrew seemed not to be as important as the other three became.  BTW, the Sea of Galilee and the lake of Gennesaret are the same place and indeed it did have multiple names.  The response of these early disciples only makes sense to me if they had previous encounters with Jesus.  For a complete stranger to come up and call them to drop everything and follow does not make sense.  John provides some insight into that.  Andrew, and another man (likely John), are described as followers of John the Baptist.  The Baptizer sends them after Jesus, and after spending time with Jesus, Andrew introduces his brother to Jesus.  John may well have done the same thing and choose not to record it.  That then provides a basis for Jesus coming and calling them to leave their boats.