Ok, that case has the camera/flash cutout way to "tight" or "close" around it. So when the flash goes off, the edge of the case (which looks at least to be 2 to 3 millimeters thick) will reflect the light and bounce it towards the lens. The lens is actually expecting the light source to be coming from straight ahead. But this "off angle" light is coming in almost flat from the side and at a very high intensity. The CCD (camera's eye) tries to process it along with the rest of the light that it is seeing. And if you look really close, the majority of the "light bubbles" are on the left side of the photo which is where the flash is positioned.
When you get a chance, you should take a picture with basically the same night condition with the case on and off. Odds are the picture is going to clean up really well with the case off.
The case I use is
Amazon.com: OtterBox Commuter Series Case for iPhone 5 - Retail Packaging - Bolt: Cell Phones & Accessories and you will notice that the cut out is a lot larger to cut down on the flash issue. Otterbox learned this the hard way when they tried to use their iPhone 4 design on the improved 4S camera and flash. They ended up switching a lot of cases out in the early days of the 4S. I was one of them