I just got back last night from several nights at the hotel. Overall I enjoyed it.
Issues we noticed:
Pool needs to be heated. (Especially Adult one)
More hooks for towels in bathroom
I hated the sink faucet how it was so close to side of above sink bowls. Don't like always hitting my hands on sink when I wash them.
The room fridges are packed with over priced drinks and no room for the complimentary water they give you let alone anything else you may have.
Fridge had beers in there but no bottle opener. I ever asked for a opener from bar and they didn't have available one for room. So how do people drink those beers? Silly.
I think some of the walk ways could have been done better to have easier access from rooms to pool/beach areas.
I also think the railings on the balconies should have been glass vs a high metal one that blocked much of the view when sitting down.
The food is EXPENSIVE. Like stupid expensive. Even the drinks by the pool are expensive. A $15 cocktail ends up being $20 after tip/tax/service charge.
They really should add a mid level dining option that serves all three meals. We avoided breakfast because most options would have put us at roughly $100 for breakfast.
A $7 carib ends up $10. Caribs at almost every other bar is $2-$4. ($1.50 at grocery store)
I thought it was weird how the restaurants would charge $10 a bottle of water when they gave you complimentary bottled water in your room (unlimited) for free.
I think the restaurants should reduce prices on their starters/desserts at a minimum. The sides and entrees aren't that off base but $20+ for a small soup is too much.
I was upset I got late checkout and my room key was deactivated an before we were told it would be. And at that point we were in a rush to get showered before flight.
Place is secluded and only has access to Reggae Beach Bar and Spice Mill otherwise you will need car or taxi and Taxis are expensive.

Liked/Tips:
Loved access to SPA. Felt we were only ones really using the sauna and plunge pool the whole trip. Though many times they had the rooms turned off.
SPA has nice tea and fruit.
I had no issues with service. Service was near perfect by pool and restaurants and bars.
Everyone on property was very friendly.
Manish at Great House bar was great and made some great beverages.
StoneBarn was best meal.
Track down Banton for Taxi service. He was super friendly and much cheaper than some other Taxi providers. (Elvis was quoting MUCH MORE)

Overall I would go back but in no rush. We did go to ShipWreck bar and learned that it is closing next week and a Ritz Carlton is being built on that side of the island.
Given how the Hyatt only had 50 guests that we ever saw during our stay I think the added options are going to hurt the Hyatt. They should reduce their room rates and prices to compete.
No way I would justify $800 a night + the extra costs of eating at resort which you are almost forced to do. (Due to secluded nature of it)