The gay stuff was hinted by the producers a long time ago.
As for arguments and stuff - there's a lot of questionable stuff that goes on in this ship, so it sort of makes sense as to why not everyone is happy about it.
This is not a flagship, but rather a ship where a lot of federation dirty stuff occurs. It reminds me of the ship Riker served on, where there was a mutiny (only there, Riker supported the dark side). Given the existence of that ship in the ST universe - with a canon story about an actual mutiny, I see nothing about this ship that's not ST. You are simply seeing another side of the ST universe, one which is not clean and dandy as is the case with ST flagships.
Point being, I actually like this series - it's gritty and it shows the darker side of the federation. I also like the continuous storyline. It won't make as much money as STTNG did, because it won't be able to milk money via reruns (most series with continuous storyline setup don't do well in reruns - so the money milking is done only via the first run), but I suspect that the first run is going to be by far better received than any other ST show prior to now.
Oh, and this tv show is miles ahead of the crappy ST film reboot series in terms of writing/acting and directing.
The single problem I have with this show (aside from being so grimdark they literally have "black alert", black badges and a captain with a special condition that requires dark moody lighting on his ship) is that it beatrs the name Star Trek.
Ironically, The Orville has proved that you can make a show heavily based on/influenced by Star Trek and still create an original universe, so I wish Discovery had done that instead.
To be honest, it feels far more like the universe (and art direction) of Mass Effect or tone of NuBSG anyway. Making this an original universe would require only changing a few names and maybe giving the Vulcans a different hat to "logic" ("science", perhaps?).
Getting rid of the thin tie to Star Trek continuity, especially when they clearly don't want to honor it anyway (holodecks and holo-communications? Starburst replacing warp drive? Klingons at are nothing like Klingons? A dark and almost fascist Federation?), would solve almost every complaint directed at this show.
It's not amazing, but its a decent enough sci-fi show... but I keep getting distracted by the fact this is anything but Star Trek yet has these tiny references or names from it.
I'm pretty convinced this is not the original show's timeline, but that we'll end up there eventually. Maybe they'll set it up so that the events of this show become pivotal to the way things were in TOS. Think about the mysterious bird of prey flown by T'Kuvma and his group - it's the only one with cloaking tech and none of the crew on board seem to be scientists, yet the ship is clearly of Klingon design. More like the birds of prey we're used to seeing. So where'd they get it?
We already know from TNG and DS9 that to regular people living in the Federation Starfleet and its officers have a squeaky clean, Boy Scout reputation. Despite the no-money theme of government service we know other people (including humans) engage in commerce. There are shady businessmen, even organized crime syndicates. And the Federation government itself has a dark side. The agency Section 31, which was written into a classified part of its charter, whose oversight is unclear - maybe even nonexistent. They do all the things a covert intelligence division would be expected to do. Conduct surveillance and infiltration, recruit civilians to help them, even conduct assassinations or other attacks that one might consider terrorism, all supposedly in the service of Federation interests.
There's always been plenty of the grunge of real life in the ST universe. It's mostly not been a focus, although DS9 and Enterprise showed more of that stuff than the other franchises. Credit advances in special effects for the fact that current sci-fi shows often feel more like actually being there and less like movie sets. Granted there is a conscious effort with Discovery to make the mood darker with a hint of looming menace. Including a captain who's slightly unbalanced. Or maybe more than slightly, we can't really tell yet.
The idea appears to be to emulate the gritty drama and dark tonal qualities of edgy TV dramas like "GoT" and "Westworld". They appear to believe they must apply a framework which copies these shows and interpret it in terms of Star Trek symbols and general narrative. This is why this show's Klingons look "demonic" and the crew of our heroes is in perpetual crisis.
I do garner some enjoyment from watching the show but strongly feel other shows like GoT etc are their own things - there is no need for the ST Discovery producers to riff off their popularity. They need to decide seriously whether ST is distopian or utopian, and not pretend otherwise by claiming falsely they doing one or the other. ST should be accepted on its own terms.