Continuity mistake: The position of Rey's right arm changes between the two first shots after we get to see BB-8 thrown to the ground in Canto Bight. (00:55:15)
Continuity mistake: After the scene showing the First Order ships appearing behind the Resistance ships, when Poe Dameron says "It's Snoke's ship. You gotta be kidding me!", the immediate next shot shows him further away and facing a total different direction from Admiral Ackbar. (00:26:30)
Continuity mistake: When the light saber breaks in half, Ben is thrown to the left of the throne while Rey is thrown to the right. Once Ben wakes up, he is on the right of the throne, exactly where Rey was when she refused him. (01:51:50 - 01:55:10)
Continuity mistake: When Rey meets Luke for the first time, the sun changes between shots.
Continuity mistake: While Rey is practising with the pole and the lightsaber, the sun changes between shots.
Answer: He knew that his blue lightsaber still existed because Rey brought it to him. He chose to show the blue lightsaber because it belonged to Anakin and Kylo Ren was obsessed with it. He knew that Kylo Ren would be angry at Luke wielding a lightsaber that looked like Anakin's and that rage would help keep him distracted. Here is a quote from Rian Johnson regarding this: "He knows that Kylo's Achilles heel is his rage, and so that's why he kind of makes himself look younger, the way Kylo would've last seen him in their confrontation at the temple, and that's why he decided to bring Kylo's grandfather's lightsaber down there - the lightsaber that Kylo screamed at Rey, 'that's mine, that belongs to me.'"