This will be a somewhat compact review and comparison to the HiFiMAN HE-400, they're roughly the same price around here. Starting with some pictures.
 

 

 

 

 

 
Accessories
While I don't consider accessories that important I guess I should mention them. K712 comes with a straight and a coiled cable, 6,3mm adapter, and a carrying pouch.
HE-400 comes with the stock cable, 6,3mm adapter and a carrying pouch.
 
Comfort
The comfort of the K712 is good. The headphones weight is 235g which is very light considering their size. The self adjusting headband works well and the earpads feel nice on the skin. I don't think the fit is too loose despite having a small head. During the first hours of use there is some pressure building up on the head from the headband, but that disappears after a while when it adapts to your skull.
Compared to the HE-400 they're obviously much lighter, HE-400 weights 440 grams which is almost double up. The headband on the HE-400 is very well designed though, and I don't have any comfort problems with them. So apart from bulkiness HE-400 is just as comfortable. Both stock earpads are fine too although I know some people don't like the HE-400 pleather pads, if that's the case then you probably like the K712 pads more which is soft memory foam.
 
Build quality
While the build quality in general is good, the K712 does feel a bit plastic considering the price. Especially the bows that connect the cups feel very fragile. The headband and cups themselves are good though, and the mini XLR connector for the cable works well. The stock cables that come with it are good.
In comparison the HE-400 is built like a tank, but the coaxial RF connectors are bad and the stock cable is extremely bulky.
 
Sound
 
Sources: CA Dacmagic Plus DAC, Lake People G109-S headphone amp
Files: My own FLAC library and some Spotify Premium streaming
 
First I'll focus on the K712 and after that a comparison.
 
As a whole, the sound provided by the K712 is impressive. I never really find it to offend or do something bad. It does expose bad recordings though, no way around that.
The bass is very well controlled. With music where slam in the bass is not intended you get none, zero. However, try turning up some Infected Mushroom or Ludacris and you will be treated with some serious rumbling or impact, depending on the song (for an open headphone). The presentation is very convincing on "Ludacris - How Low", I can dig out all the low frequency details in the background and the rapping is in perfect balance with the beat. With "Koan's - Selena's Song" it's very easy close your eyes and be carried away by the firm bassline backed up by the deeper rumbling and the ambient sounds, I imagine this is very close to how the artist wanted it to be.
Varieties of rock is probably their strongest point for me though. The balanced yet slightly warm presentation together with the rather wide soundstage is a real winner. In "Dayshell - Avatar" I can separate instruments very well and get a sense of how the song was recorded, but it doesn't get too analytical, it's very easy to still simply "enjoy the ride". 
With metal you do run into this problem where a large portion of the music is rather badly recorded and mastered, and the K712 does expose it quite effectively. When it's good it's really good though, as an example my In Flames Clayman and Reroute To Remain rips sound brilliant. I do occasionally wish the drums had a bit more "kick" in them though, something the HE-400 has spoiled me in.
The K712 does vocals so well that I can really appreciate music like Celine Dion's despite I don't normally have any interest in it. Material like the old Nightwish with Tarja Turunen sounds fantastic.
Regarding the treble there isn't much to point out. It's smooth, it's good. No fatigue, no emphasized sibilance, amount is just right.
 
Not much to add. But yeah the sound is great. To counter all this praise, I do find the sound gets a bit "too secure" sometimes. It's like, you listen, and you know it sounds great, yet it's a bit boring at the same time. But that's probably inevitable with something that performs so even. I think a 4/5 star rating is fair, could maybe be 4½, but it loses a bit on the build quality, and on price. I haven't actually compared it to the older models, but if there really are changes made that qualify a ~250€ rise in price I think AKG should make that more clear. On the other hand, they clearly compete with the HE-400 that are priced similarly, so...
 
Comparison to the HE-400
When you compare these two headphones, the weird V-shaped frequency response of the HE-400 is very noticeable. The HE-400 has a great bass presentation in my opinion, and the texture on drums is brilliant. On the same time, this combined with the rather small soundstage gives you this very intimate and warm sound that can be a bit too much. Vocals also sound a bit strange on the HE-400 when compared to the K712, this is probably related to the dip between 5-6 KHz. HE-400 also has slightly more emphasis on treble, especially sparkling sounds like cymbals, sometimes this works out great, sometimes less so. HE-400 definitely has a higher fun factor, so this does boil down to taste. I would still say though that the rock solid performance of the K712 makes it better overall. There is slightly more sibilance on the HE-400.
 
AKG K712: Is more neutral, has a larger soundstage, is an more even performer.
HE-400: More bass impact, slightly more treble, does some material very well while falling short on other, more forgiving with bad recordings

I got to try these out when my brother bought them for his casual computer use.
 
The headphones are very light, and have quite comfortable cloth pads and headband. They are made entirely of plastic, which at least doesn't feel to be of too high quality. I can obviously not comment on long time endurance. Visually they do look quite appealing however.
 
As my reference pair in this test I used the Beyerdynamic DT-770 80 ohm headphones. Note that I said reference, I didn't directly compare them since that would obviously be unfair considering the DT-770 costs twice as much. Only FLAC files were used, with a Cambridge Dacmagic Plus as source.
 
Overall the sound is quite good considering the modest pricetag, nothing is overly present or completely lacking. The bass hits by a satisfying amount without dominating, lacks "texture" though. The rest of the spectrum is nothing special, it just "does its job". The product is a slightly muddy sound to my ears, but after listening to them for awhile the brain gets used to it.
 
I would not mind having these with me on the go, they're definitely good enough for that. In any kind of critical listening there are many shortcomings, but hey, you get what you pay for.

Used with studio monitors and Beyerdynamic DT-990 250 ohm headphones.
 
Nothing really bad to say about this DAC/Amp. The build quality is high, size is small, it drives all headphones I tested it with well. No flaws in the audio quality, looks good, gives you a volume control not only for your headphones, but for your speakers too which is nice if you use studio monitors with separate pots on the backs of the speakers. It's also worth to mention that it accepts digital input from USB, or optical toslink.
 
So if you need an affordable DAC with RCA outs and an adequate headphone amplifier built in, this is a great alternative. 

Build quality is very good, they do feel "premium". The finish doesn't attract fingerprints which is nice.
 
Comfort is good, you do feel the headband putting a slight pressure the head after a longer session, but it's not bothersome. The velour pads are nice and the ears do not get warm.
 
The sound signature is very V-shaped. They have a lot of bass especially for an open headphone. It's a quite weird experience at first to get this much bass and have the quite large soundstage and bright treble, all at the same time. At first I really liked the sound, but after a longer listening session problems start to become more obvious. The bass does overshadow the quite weak midrange, it's not that apparent with all songs but quite so with others. The treble, while being really crisp and clear, can get quite fatiguing after some time especially if you want to crank the volume up. The sound is also very sibilant, any existing sibilance in the material will be reproduced and probably even a bit amplified. Some like this, others can't stand it.
 
If you don't mind bright treble and sibilance, and want a quite unique and "fun" sound with lots of bass, yet airy and open, then these are a great option. If you want a balanced soundsignature that performs well with everything, you probably want to reconsider. I'd consider them working well with pop, electronics, metal.