The show screws up master chief's character too much. Not just him revealing his face to Kwan, heck he even participates in battle without his helmet on

,but by how quickly they focus on his humanity. This was built up over the course of multiple games and one could say mostly due to the change of developers. But in this show it's rushed and feels fake. This should rather have been done more towards the end of the season.
Would improve the show if they have Kwan die off in the next episode or two, although I have a suspicion that she still has to play a very important role
The human among the covenant is just plain retarded no matter how you justify it. This is a much bigger issue than the helmet or MC's rushed humanity IMO.
At the moment the stakes in the show doesn't feel very pressing. It would be useful if they show the extent of the war with the Covenant and not just focus on this little sector of space.
As for what some have mentioned with the FTL on small ships. No that is not in any of the books. They just want to follow a more Star Wars approach like the Mandalorian. Possibly using this mechanic with MC in future episodes.
In a sense this is what this show is, Star Wars in Halo garb.
Speaking of Star Wars, at least we get to see finger swords and worms...
The references to actual Halo lore is very superficial. The nitpicking can go on for ages, but the creators did say this will not follow the books/games. That said overall they did make it look good, baring a few scenes that look bad etc.
Most Halo fans that end up enjoying this, do so by knowingly viewing this as non Halo.
The question is, if you from the start plan not to adhere to the lore, except in the superficial sense, then why make the show in the first place? The obvious answer is name recognition, but that's a very shallow reason.
All in all even if you strip away the Halo veneer it's still a meh show, marginally better than Boba Fett.