In "The Cage", they go to red alert and call the captain to the bridge, fearing an imminent collision...from a radio wave. It's so absurb it's ridiculous and should be ignored as hard as possible.
That's not an accurate characterization of the scene. Rather, they initially thought something was approaching on a collision course, but then discovered it was just a radio signal and therefore harmless. As Pike said, old-style distress signals like that "were keyed to cause interference and attract attention in this way." I take that to mean that the radio signal was designed to disrupt sensors and trigger the ship's alarms (including its collision alarm), sort of like how a strong vibration sets off a car alarm.
In this episode, they deliberately go to warp to blue shift a long faded transmission back into something that has red shifted from distance decay.
Hmm, that's an attempt to use real science, but mostly nonsensical. Something within the galaxy probably wouldn't be moving fast enough away from us to redshift that much, and it wouldn't increase over time, I don't think. And going to warp wouldn't fix it if it were; impulse speed would be more than sufficient.
I have to admit one of the problems I had with Discovery and trying to think of it as anything other than a reboot is some of that. If there were emergency force fields available why was the Enterprise relying on the more primitive emergency bulkheads?
First off, a solid wall is always going to be better than a force-field, because it doesn't cease to exist if the power goes out. Sci-fi likes to use rays and fields to do things that good solid matter does better for the sake of seeming "futuristic," but it's lousy engineering.
More to the point, though, when did we see the
Enterprise using emergency bulkheads, except in TWOK? And we saw plenty of force-field use on the ship in TOS, notably in the brig, and in the field Spock rigged to contain Charlie in "Charlie X." Not to mention the deflector shields, of course.
Another biggie for me was how the Discovery crew were nonchalantly beaming to different areas of the ship like it was nothing. Scotty was pretty specific during the original series that intra ship beaming was incredibly dangerous. Yet the Discovery crew did it without batting an eye....now if it was just not done and nothing was said about it then ok, not a big deal.
Yes, that does annoy me. But Trek has always had continuity errors on that scale. TOS contradicted itself on many occasions, and the movies, TNG, and later shows all had further contradictions. I've been seeing this since
Enterprise (and it goes back to the original movies and TNG too) -- there are always fans who react to the latest continuity errors as if they were the first of their kind and required shunting the show off into a new universe, even though they're no bigger than the continuity errors we've been getting in Trek since the beginning. Trek has never been a perfectly consistent universe, because a bunch of different people have been making it up as they went.