Contradiction with 1 Samuel 17:50
Contradicts by stating David killed Goliath with a sling and stone, without mention of lion or bear.
1 Samuel 17:50: So David prevailed over the Philistine with a sling and with a stone, and smote the Philistine, and slew him; but [there was] no sword in the hand of David.
Contradiction with 2 Samuel 21:19
Contradicts by attributing the slaying of Goliath to Elhanan, not David.
2 Samuel 21:19: And there was again a battle in Gob with the Philistines, where Elhanan the son of Jaareoregim, a Bethlehemite, slew [the brother of] Goliath the Gittite, the staff of whose spear [was] like a weaver's beam. [Jaareoregim: or, Jair]
Paradox #1
One possible historical inconsistency related to this part of the story of David and Goliath is that there are different accounts of David's introduction to Saul. In 1 Samuel 16, David is introduced to Saul as a musician who plays the harp for him. However, in 1 Samuel 17, after David defeats Goliath, Saul does not seem to recognize David, asking about his family background. This presents a contradiction regarding how well Saul knows David and when he first meets him.