Of all the fan debates currently going on surrounding Star Wars: The Last Jedi, a lot of the conversation surrounds Luke Skywalker's confrontation with Kylo Ren at the end of the film, specifically, the lightsaber that Luke is using. Shouldn't seeing Luke with that lightsaber been a huge clue to Kylo Ren that something was up with Luke? According to Rian Johnson, everything Luke does here is done specifically to mess with Kylo's head and keep him off balance, including appearing to use the lightsaber that Ben Solo thinks he has a right to, against him. According to Johnson...
[Luke] is basically tailoring this projection to have maximum effect on Kylo. 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.'
The issue at hand (and let's call this your minor spoiler warning) is that the lightsaber we see is not the green one that Luke was armed with the last time we saw him duel in Star Wars: Return of the Jedi, but the blue blade of the Anakin Skywalker saber. Overall, Rian Johnson's explanation makes a lot of sense. The fact that Luke Skywalker isn't actually there, but is instead using the Force to project himself across the galaxy, means that he needs to keep Kylo Ren on his heels. The entire purpose of what he's doing is to act as a distraction, after all. The best way to do that is to piss Ren off, which is something Luke surely knows isn't actually that hard. Seeing Luke at all, looking just as he did the last time they saw each other, has Ren furious so by the time he sees the lightsaber, he's already not thinking clearly. If he were, he'd probably wonder how Luke got the lightsaber, but that's just not where his head is at.
Of course, that lightsaber isn't exactly functional, and shouldn't Kylo Ren know that? Rian Johnson points out to IGN that the answer to that question is actually no. The audience sees the lightsaber broken in two, but all Kylo Ren sees is a bright flash that knocks him unconscious. By the time he comes to, the lightsaber is gone, and so Ren doesn't really know what happened to it, so the fact that Luke has it isn't entirely impossible from his perspective.
The audience, however, knows more than Kylo Ren and so it's likely many seeing Star Wars: The Last Jedi for the first time did wonder what was going on with the lightsaber. I certainly did. Of course, it's unlikely that people would guess what it was they were seeing, since Luke is exhibiting Force powers that we didn't know were possible.
I can't really argue with this explanation. It makes sense within the context. Now that we have that answer, we can move on and argue about the dozen things people have issues with.