I haven’t played much, but here are the biggest takeaways I have so far:
Maps: I like the maps they’ve provided so far, but I would like to see a couple larger, more open maps added to the mix. Perhaps one or two that are less symmetrical. Right now, Empire/Eden and Truth/Regret tend to feel a lot like Haven and Abandon, respectively. Truth may be a bit closer to Adrift, but the similarities to me are pretty strong.
Weapons: Damage consistency with all weapons is an issue. I’ve been two-shotted with full shields by a BR on many occasions, and the AR seems to go from extremely powerful to a pea-shooter at any moment. The SMG is a bit overpowered at mid-range, and with both full-auto weapons it seems that once you get hit you can’t escape or dodge, almost like there’s a target-lock on you. That MIGHT be my rather meager skill at work, but hey, I’m spitballing here. If I get into an AR duel, I would like to be able to dodge out of the way and not feel as if the bullets are following me through my dodge. Energy Swords are great, but there seems to be an inconsistency with lunge distance. It should be closer to the AR’s effective range (which also is a bit inconsistent) but it varies. Grenades seem OK, not dangerously overpowered like the pumpkins from the Halo Reach beta, but something about them seems a little off. I can’t put my finger on what it is though.
Controls: Controller functions are fluid and familiar, but at the same time it feels like there’s just too damn many of them. Now we have thruster pack, ground-pound, sprint, and Smartlink/ADS (depending on the weapon, I’ll get to that in a minute) and I hate fumbling my controller trying to find the right function. I’ve tried a few different layouts but with all the options none of them feel quite right.
Abilities: I like the abilities they’ve kept, but I almost think they’d be better if the player could choose the ability instead of packing them all in. That gets too close to loadouts, though, and I didn’t like those too much.
Overall, I’m pretty happy with how the game feels, even though I suck at it terribly. I absolutely love Breakout, it may even replace SWAT as my favorite gametype, but I would have to play SWAT itself to make a proper comparison. Slayer games feel like classic Halo, which means I find myself repeatedly getting my backside kicked, but they’re still FUN. The pace of gameplay is faster than previous Halo games, even Halo 4, but it doesn’t completely break the game. I would like to see some gametypes that evoke classic non-sprint/thrust Halo gameplay, but only as an option.
Now, onto a couple of specific complaints:
Most important to me, the ADS look to the scoped weapons simply has to go. It makes no sense to get the Smartlink effect when using the AR or Magnum but you suddenly see a scope frame with the DMR/BR/Sniper. I won’t get into the lore science of Smartlink, but scope frames are contradictory to the function and shouldn’t be there. It also takes away a significant part of what I liked about Halo: No clutter on the screen when scoping. Oh, and that weird-looking red-dot-like horned scope on the BR? Get rid of it, 343. Please. 
Party pull: When the party lead wants to back out of a lobby, it should pull the entire party out. I’m sure this is just a beta issue and will be fixed, but I would like to see that happen before the beta period ends.
Mute game chat: Previous Halo iterations had the ability to mute game chat or assign it to headset-only. I would appreciate the return of that function as well. I don’t like sitting in a lobby and hearing some anonymous 12-year-old who learned new words cussing up a storm while my son is next to me watching me play or in a game with me. Setting up a party is a pain on the One anyway, so it would be nice to have this ability back.
Callouts: I don’t mind the generic callouts so much, but they really don’t work properly right now. I hear “BOOM!” then “Grenade, look out!” right after. Or a teammate yells “Grenade!” and you hear the boom on the opposite side of the map. They feel like filler more than anything. Halo multiplayer doesn’t need filler.
So those are some of my random thoughts about the game so far. I hope to add a few more impressions as soon as I play more games.