Long post is long.. read carefully
Source: FAQ: Consolidated thread w/FAQ on 61xx switchable graphics + advice to potential 61xx buyers

UPDATED 6/30/2011

I thought I might centralise the discussion for those who ask as whether they should buy the DV6/7 61xx or refund their order as I think the switchable graphics thread has become a little confusing for newcomers.

Status of switching on 6770m: As it stands (as of AMD catalyst driver release 11.6) graphical switching for programs that use OpenGL as their SOLE graphic engine will not run on the 6770m discrete graphics card (dGPU). Instead, those programs will only run on the Intel HD 3000 integrated graphics card (IGP) and therefore will not run optimally.

As you have probably gathered MANUAL SWITCHING DOES NOT WORK ON DV6/7 61xx AT ALL so we can't override the dynamic switching in place.

OpenGL programs that will use Intel HD 3000 integrated graphics

• Minecraft
  
• Adobe CS Suite
  
• Amnesia: The Dark Descent
  
• Quake Live
  

Not an exhaustive list by any means. There may be a number of graphical creation/manipulation/3D modelling programs out there that also run solely on OpenGL and will therefore not run well on the 61xx. but bear in mind the following:

• Most Windows games run on DirectX which works fine with the 6770m.
  
• Most modern Windows games that can run on OpenGL will also have the option for you to run through DirectX.
  

Other annoying issues:
Currently, the 6770m will not register clock and memory speeds properly on monitoring software such as GPU-Z. Benchmarking/stress testing software such as Furmark will not run well at all (OpenGL) and if you bench with any 3DMark software the results screen will show that it's just tested your Intel HD 3000 (which it hasn't, it'll have benched your 6770m, but because under the muxless design, your Intel IGP is always on, it recognises the IGP first, and not your 6770m - more on mux and muxless designs below).

Also, you cannot overclock the 6770m in the 61xx whereas you can in the 6xxx range.

Does the switching problem only affect 1080 resolution models?
No, 768 models are affected too.

Should you buy/return?

If you:

• Surf the net and play modern Windows games (with exception of Minecraft) -You're fine as the 6770m will cater for most of your needs but you have to understand your dGPU is crippled to an extent should you ever need OpenGL acceleration.
  
• Play games and use graphical content creation software such as Adobe's suite of products - Problematic - would definitely not buy or would return.
  
• Do a mixture of everything above - if you have programs that run on OpenGL my advice would be not to buy. Why buy a laptop that's not working at its full potential?
  

When will HP or AMD fix this issue?
This is the hard part and it's anybody's guess at the moment as HP and AMD have not made public they are aware of this issue. Through the complaints that all of us have fed back to HP and AMD I'm sure they're aware of it. Some hope that by the release of the 11.7 catalyst drivers due out in July this may be fixed but it's all speculation at this point.

But this disclaimer on AMD's switchable graphics web page does not give hope to a resolution anytime soon:

"With AMD Dynamic Switchable Graphics technology, full enablement of all discrete graphics video and display features may not be supported on all systems (e.g. OpenGL applications will run on the integrated GPU or the APU as the case may be). Always check with your system manufacturer for specific mode capabilities and supported technologies."
AMD Dynamic Switchable Graphics Technology

Are other laptops from other manufacturers affected in the same way?
Yes. Any new laptop with the AMD muxless graphics switching design will have this problem, regardless of brand.
Here are a few examples:
ATI GPU doesn't work on E520 - Lenovo Community
IdeaStorm | Update Vostro 3550 AMD 6630/Intel HD 3000 Switchable Drivers

What is mux (manual) and muxless (dynamic) graphics switching? Is it a matter of it being a driver or hardware based issue?
bsoft explains it better than I can here - edited for brevity and accuracy:

Any link to the video? i want to try with my Chrome.