Two twitch streams found each other in the game and tried to go to the same spot at the same time to see each other. They couldn't see each other. They tried rebooting, relogging in, making sure both on PS Plus, moving around, going somewhere else. They tried several times, no luck
Then someone packet sniffed their PS4, and noticed no info being sent about their in-game location to NMS servers. People thought it proved no MP support, but other suggest that its likely because the servers don't require clients to send their location over and over again uselessly, and maybe only requests location when it knows two players entered the same system. Nothing conclusive yet, expect either those two twitch streamers encountered a bug, or the feature is off for now, or Sean lied.
Then someone tried flying to a sun/star, but after 2 hours, the game bugged out, their HUD and ship glitched and disappeared, which turns out to be likely due to a floating point error from being at x,y,x coords that are so high, precise math can't be done, causing graphics to be drawn badly. No way of getting to a star, turns out every solar system in a galaxy is just its own system skyboxed with the nearest sun (light source) pasted on a wall at infinity. Much less freedom.