Beacons and New Stars
In ep. 1, the Klingons create a new star/beacon that instantly calls/signals Klingons from far and wide - presumably over distances of many light years. That's impossible. Starlight would take years to propagate (or even just hours if the other Klingons are, as it were in the same solar system - light from our Sun takes over a hour to reach Saturn for example).
Later we hear from Sarek who's thousand of light years away (over - wave hands! - standard Star Trek faster-than-light communications systems) that he can already *see* the new star/beacon in the sky. This is no-ifs-ands-or-buts impossible.
I'm prepared to cut sci-fi on TV and in movies considerable scientific slack, but the Star Trek universe has historically tried a little bit harder than this to maintain a veneer of physical plausibility.
This may be the least of Star Trek:Discovery's problems right now, but it's significant nonetheless.