7)  Make sure that PS4 is reasonably priced. 

I think that should be way higher up on the list (probably number 1 or 2).  Isn't that the main point Sony should have came away with this generation?  Who wants to drop more than 500 on a video game system?  Not too many people did.

better gpu

ps1 had inferior multis they few that were at that time with n64

ps2 had the inferior multis against the xbox

ps3 does again

free online

low failure rate

at least ps3 B/C

continue to provide great 1st party SW

almost every thing said already... also make sure your effort to keep playstation out of pirates is alive...

1) One SKU at launch.

2) Create the right balance between camera and controller controls.

or

2b) Create a controller to enhance 3D gameplay.

I wrote a thread a while back about what ps3 should have too.

The list was something like:

solid state or flash drive HDD
Bluray drive
simpler cell architecture.
ps2 and ps1 emulation (no ps3 emulation. People need to buy a ps3 to play them. Similar to what they did this gen.)
motion control 
USB controllers and wireless
A dreamcast VMU type of device that records your settings/ save games and does other things with transportability.
3D capabilities

Most of this stuff would be doable at the current ps3 cost. By the time ps4 comes out, it should be ~300$, no more.

And yeah, a really, really capable GPU. And leave out the bottlenecks.

But the RSX GPU and CELL work together for the Graphics horsepower of the PS3 so the PS3 can do equal or better then XBOX 360 with mutiplatform Games FFXIII, Castlevania and Vanquish are good examples of this.

What I think that Sony should do is if possible make a PS4 with a powerful CPU but a Med-End  GPU. Then if you want you will be able to buy and connect a PS3 official GPU in a external port. They could make a PCI- like external port for this GPU.

This should keep PS4 in lower price range, but if you are hardcore you can have awesome graphics too.

But only if Sony finds a solution for Developers to don't have almost any extra work. It's not impossible.

Maybe this external GPU could be a replica of the internal one, to make a dual-gpu system.

Some people think the most important thing is price, but I think the most important factors are

A reasonable price (maybe $299 for entry model and $399 for one with a much larger hard drive)

full backwards compatibility with PS3, PS2 and PS1

Good launch lineup (GT6, LittleBigPlanet 3, new IP's...something like that)