CPU is not that important for 1080p decoding, but you don't want to try it on an Intel Atom. The graphics are more important now. For multimedia you want a laptop with a graphics card by ATi or Nvidia, no question about it.
AMD's offerings as you may recall pale in comparison to the Core 2 Duo. Recently though the Athlon II and Turion II processors have hit the market, and they are very competitive with Core 2 Duo processors, and laptops with these Athlon II or Turion II processors cost hundreds less than their comparably-performing C2D counterparts.
Also, the weakest graphics option you can get with them is the Radeon 4200. Hands down, it is much faster than Intel's integrated graphics solutions (which is what you get with Core 2 Duo laptops unless you shell out for a discrete graphics card), and the Radeon 4200 has UVD2 which does full bitstream decoding of H.264/MPEG-4 AVC, VC-1, and MPEG2 video streams. It also supports dual video stream decoding and Picture-in-Picture mode, so it's Blu-Ray Live compliant.
At this point I would not recommend getting a Core 2 Duo laptop because you will pay more for a processor that is equivalent to the Turion II M500, and the video performance from Intel is much weaker than the Radeon 4200. Add $150 or more (to the already high-priced C2D laptops) and you can get a Core 2 Duo laptop with a video card equivalent to or faster than the Radeon 4200. But at this point it would be needlessly expensive and comlicated just to get an Intel laptop that rivals AMD's mobile offerings in terms of multimedia capability.
Your other option is an i3 or i5 laptop with a discrete card, and I honestly haven't looked at how much these cost but I know they will perform better than Core 2 Duo and AMD's mobile processors. Then again, you don't need extreme CPU power, or even a discrete video card. Unless... do you plan to do some heavy gaming on this laptop?
...some of the recent, nicer integrated graphics by Intel are capable of 1080p I believe, but no fancy features as far as I know. I haven't looked into specifics because I generally view Intel graphics as fairly worthless, but I don't believe the hardware decoding is as sophisticated as Nvidia or ATi's. I think these integrated chips from Intel have 'HD' somewhere in the model name, implying they can play HD video, and I'm not positive but I believe you can only get them with i3, i5, or i7 laptops.