What you'd expect to happen when you place an item frame on a block is for it to place and appear where you right clicked.

However, in large coordinates, usually around 20 million, the item frames are placed to the left or right of the block when I right-click on every other coordinate.

Steps to Reproduce:
1. Type "/tp 20000000 100 20000000 (y of 100 insures you won't teleport in the ground, preferred to do this in creative mode)
2. Right click on the side of a block with an item frame as you normally would. If it acts normal, go directly right or left of the block and right click with the item frame again.
3. By this point, you should have witnessed the bug. I recommend to see it best that you place a 1x1 pillar of blocks. Build a wall of blocks may cause the item frame to be placed in the wall and make it harder to see this bug.

Attached is a screenshot of the bug. As you can see, the coordinates are up to 20 million and the item frames are behaving abnormally. As much exploring I've done of this, it does not matter if the coordinates are positive or negative.

Addition: This post was linked as related to a similar bug that happened in 1.8 pre releases that were claimed to be fixed. However, this bug is different, occurs in Minecraft 1.8.7, and is not fixed.