To start off I have just finished reading the player's handbook and going over the Basic Rules DM section. I have not had a chance to play the game yet and reserve the right to change my opinion of something after I have had a chance to try the system out.
Overall I am really liking the core system, During the play test I though that the flat math system was going to be annoying and make leveling up pointless but it actually works out really well. The use of advantage and disadvantage is a great way to allow for the situation to affect a roll without needing to add a ton of little modifiers and will greatly speed up game play. The proficiency system is another thing I really like, while it makes little difference at low levels it builds up to a significant improvement to your effectiveness. The only thing I don't like is that in the end you can get a total of +12 (+14 for barbarians) for a static bonus on a roll.
For ability scores this edition changed the way ability scores worked to cap them at 20 for player characters and 30 for monsters. I think this is a good change as it eliminates the need for spells or magic items to get your numbers high enough to fight level appropriate foes. My only problem with the attribute system is that if you use point buy or set scores to make your character you will barely get enough stat increases to max out two ability scores assuming you started with two fifteens. This is a problem because it also means that to do so you can't take any feats which eliminates a lot of character customization. Fighters are not affected by this as they get extra stat increases.
Multiclassing is fine, calculating spell slots is a pain but it otherwise looks fine. The way spells automatically scale with spell slot is nice and Cantrips are equivalent in power to a weapon attack means that mages won't ever feel useless. I haven't read every spell but the system seams to work fine form all I've heard.
Equipment is a nice and simplified, there are not pages and pages of weapons and armor to choose from, just a handful of distinct choices each of which is noticeably different from the others. I like this as it speeds up character creation when you choose your signature weapon. There are several pages of other items in the book, most of which look to be useful depending on the adventure. Carrying capacity has been massively simplified to 15 times your strength which I'm thankful for. Armor has max dex bonus based on class, full modifier for light armor, max of 2 for medium armor, and no effect for heavy armor. The only special material there are rules for is Silvered weapons, costing 100 gp extra to let the weapon work against vulnerable foes.
The damage system is good, critical hits have been simplified to double weapon dice on a natural 20, extra dice for half-orcs and barbarians. Damage reduction and energy resistance have been simplified to just Resistance which halves damage of the specified type. There are a few abilities that subtract a set amount of damage but they are rarer. There is about a page and a half worth of conditions both positive and negative which will make keeping track of them simpler.
The one part of the book I didn't like was the way it handles Feats. Feats are special abilities that a character can select in place of increasing their attributes. The fact that you want as many attributes to be high as possible means you will be very unlikely to take any, there are a few that stand out as good choices for every one. Alert gives you +5 on imitative checks and immunity to surprise, making the single largest bonus I saw in the book, Resilient gives you +1 to an attribute and proficiency in saves tied to that attribute, and two weapon fighting lets you do what the name implies if you want to.
I think that when I run it I'm going to have characters start with one feat and gain an additional feat every 4th level, this lets them customize without hurting their abilities. It also means that characters can start using certain combat styles before third level.
You can find the basic rules Here. This is a free download that does not include feats but is otherwise the same system.
Now I'm looking to try the system and see how many of my initial thoughts were correct.