Youtuber Ryeonham reports on his Remington customer service dealings.  Apparently a redesign is in the works for at least one part on the R51. Check out his video here:

http://www.youtube.com/watch?v=d7fNAusFyow&list=UUOvuoPY-nG-978Nmksc3-eQ&feature=share

I recommend following this guys videos for the all the latest information

Shot like a dream. Noticeably low recoil, and muzzle rise.  I would say that my R51 it is not much easier to rack the slide on than my other autos (colt 1911.45 cal and CZ-999 .40 cal).
All rounds that fired had bulged primers, didn't seem to effect functionality.  I thought all the issues I had were ammo related (I shot nothing but dirt cheap ammo, all eastern bloc; except the Blazer). about halfway through shooting  I decided to keep one round of each ammo type, and there was one FTE so Actually shot 246 rounds.

I shot the following:
49 rnds Hot shot (Steel) – 1 Failure to Ignite, light primer strike, but the primer felt recessed.
50 rnds Tulammo (Steel) – No issues
49 rnds ZVS (Brass)– 6 FTE
49 rnds Blazer Brass – No issues
49 rnds Wolf (Steel) – No Issues

So I search the web quickly today and found Military Arms Channel review and decided that it may have been more than just the craptastic ammo:
https://www.youtube.com/watch?v=aTzS4sQfn4U

MAC had a bulged case just like RyeOnHam (youtube user name of another R51 owner). I didn't have any bulged cases, nor did a shot fire while partially out of battery.  The fire arm returned to battery after ever shot with the exception of possibly the failure to ignite.

Reference photos attached to see a photo of the FTE.  It looks exactly what MAC called a "double feed" I think.  In my case it was certainly a spent case that did not eject.

http://bearingarms.com/remington-r51-first-impressions/

Though not conclusive with regard to the failures, I found this to be an interesting read.

Here are some photos of my R51 after clean and lube, before ever firing.  Everything looks good enough.  One oddity is the magazine floor plates.  You may be able to discern that the floorplate on the left has a nice matte finish, the one on the right has a polished finish which looks "cheap" in my opinion.  In the photo of the loaded magazines you may notice the plastic floorplates bowing a bit. 

https://www.youtube.com/user/RyeOnHam

He has some slightly long winded but detailed videos regarding the R51.  His videos on the gun are by far my favorite.  I haven't shot mine yet, but after watching his video, I confirmed that I can pull the trigger while the gun is out of battery on my R51.  This behavior caused RyeOnHam some issues while at his local range.

Another video (long) of someone having problems with their R51
http://youtu.be/1TSZmkJMBBk

I just hope that the gun runs well for me when I get it to the range.

There where two delivered to Gander Mountain in San Antonio, TX.  I picked up the last one on 3-28-2014

I hope this gun turns out to be a winner.