It's great to see the level of detailed architectural discussion this post has generated. Now, THIS is what GCA should be all about!
That being said, I'll don the battle armor and jump into the fray.
Running Deer is a throwback; a raw, creative, imaginatively bold effort literally molded out of the flat Jersey pinelands.
At it's best, it reminds one of what golf was possibly like in the 20s before modern notions of fairness and playability took over, mixed with the modern, sculpted, artistic look and daring of a Michael Strantz.
At it's worst, one scratches their head as BillV mentions and mutters, "what the @*($?"
Let's start with the good. First of all, the look is startling and clearly meant to both inspire and intimidate. Fairways generally have a good deal of movement and sometimes, purposeful obfuscation from the tee. The bunkering is raw, wild, untamed, and close to great...no...it is excellent, especially in comparison to so many bland modern bunkering styles. The positioning of the bunkers is close to random in stretches, which I appreciated for its unpredictability. The greens, very, very challenging and running perhaps only 8 on the stimpmeter, are a roller-coaster ride of various imaginative design, though not completely tied into their surrounds, nor consistent with the overall theme. For instance, it's somewhat overkill for a 480 yard par four to play to a green looking like volkswagons are buried underneath!
If it's the mark of a great course to have strong individual holes, RD has quite a number of them. The first three are all imaginative and spine-tingling, the 5th is a great short pitch par three, 7 is an intimidating but still playable mid-length par three, and 8 has a wonderful green complex that offers all kinds of pin-placement options. Heading out the back side, 10 is visually stunning.
Then we get to the most discussed holes here and I'll weigh in my opinion. 11 does have the blind water hazard the Geoffrey and Bill mentioned, and it does make it foolish to attempt to carry the bunker. However, the way the green runs off to almost a peninsula shelf in the back left makes one want to get as close to the green as possible. This is not a hole where you want to have a mid-iron approach. Instead, I believe the play is to challenge the bunker/water complex as close as possible to leave a short iron to another complex green.
12 I believe was outstanding. BillV and I talked about this today, and I understand he played what are known as the "Long Wet" tees on that hole. Simply put, that tee area doesn't work as the angle is totally incorrect. The rest of the tees are further to the left of this left to right dogleg, and effectively creates a cape carry off the tee. If you make the daring carry and keep the ball on the right side of the fairway, you have a preferred angle to the left to right canted green that sits beautifully and intimidatingly above the fairway. At 479 from the tips, it's a potential killer, but also beautiful and thoughtful.
13 is a par three that plays to 246 yards, but to a green nestled behind a minefield of bunkering and mounds to a green that is BRUTAL. Thankfully, we played at 206 yards, and it's intimidating but reasonable from that distance. It's the shortest 246 yard par FOUR I know! 
15 is one of the best holes on the course, and a great one to a green with a horseshoe feature that is brilliant. Possibly the best hole on the course, playing the second over a sandy, bunkered pit that is visually awesome and scary.
The majority of the holes are Fun, Inspired, Thoughtful, and Surprising in their imaginative and almost anachronistic shot values.
However...then there are holes like 9, 14, and 18 that are among the worst holes I've ever seen. As Geoffrey mentioned, the landing area between bunkers on 18 is 12 paces wide!! This, on a 477 yard uphill par four!!
You need to fade it slightly, there Matt?? I couldn't hit that area with a wedge?
Seriously, I hit one of my best drives of the day that had a slight draw (I'm lefty), and it two hopped into the left side bunker. From there, I faced an uphill, 200 yard, blind shot with a 60 foot tall tree in the way! AAAARRRRGGGHHHH!
Nine....This is a hole that I took 2-iron from the tee and ended up in perfect position. My options were to hit a 5 iron away from the green to the left, or attempt the 5 iron over a forest as I lay only 190 from the hole. I took the forest route and almost made it, my ball ending just short of the green. I can't describe how bad this hole is in it's present form.
14 is nearly as bad, relying once again on two stands of trees to remove options and dictate play.
The green complexes, while wonderful if looked at as stand alone entities, are not nearly as tied-in to their surrounds as they could be. All sorts of nooks and crannies and fall offs and rises really need to better integrated into the approach areas as well. Bill's comparison to the kid who dresses in a menagarie of styles is somewhat apt here.
The biggest problem at RD, however, is the fact that single trees have been left inside the fairly wide clearings in all sort of odd places. In some ways, they add a sort of Augusta-like beauty, but they are pervasive and ultimately detracting and almost silly. Potentially VERY good holes like the 10th are almost ruined by their existence within the playing areas. They become double, even triple penalties in some instances like the one I mentioned on 18.
The features on the course make RD more than interesting enough. I can't tell you how much the existence of these trees negatively impacted both the vistas as well as the reasonable options that should exist on many holes.
Nevertheless, I believe the good here is SO good that it clearly outweighs the negative by a good margin. Hopefully, the course will continue to evolve, and I will gladly join the all-volunteer chainsaw army to help make this course all that it can be.
I stand by my assessment that it's a 6. It could be a seven with a good deal of thoughtful work.
Incidentally, our other playing partner (also a Golfweek panelist who isn't particularly sophisticated with a computer) emailed me today with his rating. He has played a great number of courses, including every course in NJ. He told me he rates it between 5.5 and 6.5, so I feel that I'm in the right ballpark.
Bottom line...I definitely understand Bill and Geoff's thoughtful critical assessments and negative criticisms, and don't quite feel as glowing as Mark and Matt in the course's present form. Call me a moderate, but I'd recommend anyone travel a distance to play RD and although some holes and features WILL definitely disappoint, there are more than enough good things there to make me confident in stating that the course overall will not.