Mini ITX build urgent help NEEDED!!

It's fine, there's nothing terribly wrong with it.
The only thing that stands out as an obvious error is the 4670K (and probably the Z87) as both have effectively been replaced with the 4690K and Z97 boards.
Also the 250D isn't exactly much of a space saver unless you can fit it in a bookcase/desk/shelf etc where you can take advantage of the low height - it's very wide and in most instances this is the limiting dimension.

If you want quiet then the H100i might not be the right path to go down. You'll likely get better value and lower noise from an air cooling solution and you have a bit more control over this.

As for the overal build/budget, you can potentially cut down the cost a lot if you need to. Sticking with a GTX770 rather than pushing for something higher is a solid choice if you are staying at 1080P. You can make an argument for spending more here, or at least a higher percentage of your budget, but it's not strictly necessary.
The 250Gb SSD is likely a luxury so this would be the obvious place to save if you want to get things a little more price conscious ($1000 or so for a build like this is very achievable).

Obviously the PSU is missing too. Anything in the 500-650W range is plenty for the build you have - if you want a modular/semi-modular unit then it'll cost extra. Suitable units include basically anything by Seasonic/XFX, the Antec-HCG range, Rosewill Capstones and if you desperately want a Corsair to match your case+cooler - the HX650.

Well you aren't really saving money on the CPU/motherboard. Both are very similarly priced to their newer versions which have enough extra features/performance to make it worth the swap.

The 250D isn't particularly large in volume, but it's probably the single widest itx case on the market as it allows for a H100i to sit alongside the board. The issue here is that if you plan on putting it on a desk or even on the floor, it'll take up more effective space than most compact towers will, as they are much narrower (height is rarely a concern and depth is usually not a huge problem either).

I think you just have to decide what your priorities are, and how you practically will use the system.

As a no-nonsense, good looking i5+GTX770 build, there is really nothing wrong with what you have (though again I'd step up to a 4690K+Z97, minor thing though).

As a build focused on low noise, I wouldn't go with a closed loop cooler, I'd go with an air cooler and a substantial one at that. At idle something like a H100i still has to be pumping - a good air cooler can be almost off entirely.
Something like a Node 304+a hefty air cooler (think NH-D14 or similar) is probably what I'd use here due to the solid front, good air cooler support and integrated fan controller to have easy control over case fans.
Also worth consideration is ditching the K-series altogether. Easiest way to keep noise down is to keep temps down - a decent heatsink+fan combo on a stock clocked CPU is going to be incredibly quiet as it doesn't have much heat to dissipate. You could argue that this is a waste of money though.

As a build focused on small size, I wouldn't go with a 250D. The Node, Antec ISK600 and Elite 130 are all around the same size/shape and are likely to be easier to tuck away somewhere so might be good options. The RVZ01 is excellent for this as it'll fit more or less anywhere but it does limit you to SFX PSUs which can be seen as a negative.
The Hadron is about as small as it gets in terms of volume, it's a great option, but it does pose significant limitations to coolers and you'd ideally want to change the graphics card for a reference model too.

As a "good cooling" system, I probably wouldn't get a 250D. It's a lovely case but overall airflow isn't it's strongest area. It has decent fan support but they are all poorly located. ITX systems are always a compromise here but I'd consider the "kings" of airflow at ITX to be the Node 304 and Bitfenix Prodigy.

As a $1200-1400 gaming system, I'd spend more on graphics or less overall. Graphics cards are still by far and a way the significant element in gaming performance and most builds of this price range will be packing more in this department - likely a GTX780, R9 290 or 290X - all of which will significantly outperform a GTX770. Now at 1080P there's a solid argument for spending less money - a $1000 PC won't really perform any worse than a $1200 PC with the same graphics card.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4690K 3.5GHz Quad-Core Processor ($209.99 @ Amazon)
CPU Cooler: Corsair H80i 77.0 CFM Liquid CPU Cooler ($89.99 @ Newegg)
Motherboard: Gigabyte GA-Z97N-WIFI Mini ITX LGA1150 Motherboard ($119.98 @ Newegg)
Memory: Crucial Ballistix Sport 8GB (2 x 4GB) DDR3-1600 Memory ($77.99 @ Newegg)
Storage: Crucial MX100 256GB 2.5" Solid State Drive ($113.25 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($52.92 @ Amazon)
Video Card: Gigabyte GeForce GTX 770 4GB WINDFORCE Video Card ($369.99 @ Newegg)
Case: Cooler Master Elite 130 Mini ITX Tower Case ($34.99 @ Newegg)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($70.98 @ Newegg)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($22.20 @ Amazon)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($102.98 @ Newegg)
Total: $1250.26

There's a couple of issues.

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  ■ If you aren't overclocking then the 4690K is a total waste of money - get a cheaper i5 like a 4430/4440.
  ■ H81 boards might need a BIOS update (if they've been sitting in a warehouse for months/weeks) to accept Haswell refresh models, which is another good reason to change the CPU rather than deal with the hassle.
  ■ I'd perhaps leave out the case fans for the time being. Two sit directly above the graphics card - have them as exhausts and they will work against the graphics card fans, having them as intakes is fine but the graphics card will likely self-intake to some degree anyway. The other fan sits directly above the CPU cooler - you have a down blower so you can use this as an intake but not as an exhaust and again, the cooler should self-intake.
  EDIT -you might not even fit the fan above the CPU cooler due to the CPU cooler height. Max height available = 83mm (according to Silverstone). Cooler = 59mm (Coolermaster) Fan = 25mm (Noctua). Even if it fits it's going to be incredibly tight.
  ■ I'd be inclined towards low profile memory. I don't think it'll clip your cooler but it's going to be reasonably close so why take the risk?
  

My pet hate is build spamming without context, they might have the best build, but I don't see how that can ever be the best answer.