Shield is its own proficiency; it is not bundled with medium armor.Matt Mercer has put a lot of time and effort into creating this, but I feel it's not necessarily a 5th edition creation, more his background in Pathfinder coming through a little strong.
Firstly I'd like to see Medium Armour removed from a Blood Hunter. I think any class who gets Medium Armour is also given shields, which I don't feel fit with this character. Limiting them to Light Armour seems a better fit.
Secondly, by removing medium armour you could justify giving a third skill choice for Blood Hunter. Adding Animal Handling (most hunters need access to animals such as hunting dogs or just horses to ride the distances) and Perception.
Thirdly the Starting Equipment should be leather armour, not studded. No-one is given Studded (I don't agree with it, but the PHB is mean like that) Scale would no longer be given because they were losing medium armour proficiency.
I would change Fighting Styles to eliminate great weapon fighting and replace it with defense - I don't see any reason a hunter wouldn't be prepared to be defensive to ensure surrival as they wear down their prey.
Blood Curses is something where I feel his Pathfinder expeditions have led him to neglect how much stock 5th edition puts into Adv/Disadv. Anywhere it says "add your wisdom" really should just use the Adv/Disadv system instead.
Blood Curse of the Mutual Suffering needs a Constitution saving throw each time they would suffer the damage, otherwise it's very powerful for a multi-turn ability. I would change it to 1 turn, since it only requires a Bonus Action, and the amplify extends the duration by a number of turns equal to your wisdom modifier.
Blood Curse of the Transfusion seems like a good place to use blood rite damage, so you take damage equal to half your level an heal them for an amount equal to twice your blood rite damage, plus wisdom modifier. (so at level 20 you're looking at taking 10 damage to heal someone for 6d4+5, assuming your wisdom was 20)
Enduring Death Form seems underpowered, it would've been better to simply say "you have advantage on death saving throws."
I wont go too much into the Archetypes, but needless to say cleaning up for 5th, wherein they very rarely use "a number of turns equal to an ability modifier" anymore, so Supernal Flurry would just become 1 minute instead.
Obviously when you look at the Multiclassing box it would become "Light, Simple, Martial and one skill from the blood hunter list" to keep it in line with other classes of similar bent.
Overall I'm not sure the Blood Curses are adding much depth to the class, I feel if you eliminated them entirely the busy feeling would diminish heavily (as well as simplifying the blood rite damage dice)
I agree that the starting light armor should be leather; as studded leather is essentially the top tier light armor.
Disagree with changes to fighting styles, number of proficiencies, armor proficiencies, etc.