System Information
Windows 7 x64, Phenom II, 8GB, Radeon R9 270 (Driver Packaging Version 15.30.1025-151117a-296575C)

Blender Version
Broken: 2.77-rc2 , 2.77 02cabda (dev build https://builder.blender.org/download/blender-2.77-02cabda-win64.zip)
Worked: 2.76b (f337fea) and all earlier

Short description of error
proofpicture: http://i.imgur.com/eyUhh2o.png
rendered by BI camera fly in rotation, objects are rotated as they must, but worldmap background stay still and has no move with all

Not so short description of error
Then you use Blender internal render (not cycles - no no) , has where world texture image with Equirectangular mapping (maybe not only that i think) and Camera attached to something what has rotation ("animated" calling be?)
--> background world texture on rendered image will no has an any transformation as it rendered with simple still background cropped picture with view-mapping or some of it/

Then camera is disattached from parent is seems working right (has visual difference in angles with displayed in viewport, but for me it is not critical now )

Exact steps for others to reproduce the error

1. open attached scene
2. call render image by some standard way. wait for it stop eat CPU
3. scratch time slider some over random frame with meaning change of camera angle (seen it on viewport)
4. change Slot if render result fom 2 to some different
5. Render again and wait it
6. swap around render slots and watch - objects are rotated but background is still the same, if you repeat all steps in older builds background would be correctly transformed by rotation

*i'm not brain damaged, just bad knowledge of language, sorry