PS4
Backward compatibility
There would be cooling issues if the Cell processor was included in the system, so if it's possible to do it (the cell processor costs only like $25 now) then the PSU would be external for now until PS3 emulation can be decent enough to be released. If PS3 emulation could be decent before release of the PS4, and could get a decent amount of emulation profiles for it by launch (over 200 top selling games) like the 360's BC then I'd focus on software emulation.
If software emulation and internal BC is not realistic, then here would be an add-on module with an embedded Cell/RSX graphics chip that would connect to the back of the PS4 via an external PCI bus adapter so it can have access to the PS4's I/O and AV-Out subsystems.
The x86 architecture is fast enough to handle the subsystems necessary to emulate the PS3 properly, due to having 512MB of the memory it needs. This add on would cost about $50 and would attach itself like that ugly Nyko hard drive add on thing (plus smaller and better looking lol) or can be plugged in and hidden, whichever.
All PS4's will be BC with PS1 and PS2 games via emulation.
Hardware
Hardware is fine as is, but maybe soup up the CPU a little bit (2GHz/1GHz like you said), a Sata 6 hard drive, and MAYBE (depending on price) 2-3GB extra RAM for OS support like you said. 8GB GDDR5 though costs a TON of money, so it may not be feasible. Really though the hardware is pretty much perfect, just a little more power in the CPU. It'd be a loss but I'd include the PlayStation camera, mainly for non-gamer type games and voice recognition.
PlayStation Network
PSN is free, but super basic. Basically, you get online multiplayer, albeit not as good connections and tons of ads. Some of them even intrusive (gotta make money somehow). For example, video ads on the dashboard, and ad notifications during gameplay. And there will be limitations: no party chat for free PSN, only up to 100 friends, limiting messaging. 2 accounts per console only. Basically barebones online, but Sony can still make an argument they have free online.
PSN+ will have a ton of features. Instant game collection and discounts of course - and good ones too (way better than now). Exclusive and early released demos. Shareplay/family sharing plan. SmartMatch matchmaking/reputation system/better matchmaking period (better connections), faster downloads, ability to download multiple things at a time, party chat, unlimited friends, can change username for free once, 12 accounts per console, update in the background, no ads, ability to categorize friends, etc. etc.
PlayStation Home will be retooled as a social network for gamers. Kind of like Miiverse. People can comment on your profile/rate you (and you can dispute lol), you can put your favorite stuff on your profile plus a wish list, a list of your trophies, custom background/pictures for profile, basically a far better Miiverse with Twitter/YouTube/Facebook intergration as well.
Controller
Make it super comfortable, put the analog sticks in the right places (like Xbox/GameCube), touchpad will be a touchscreen instead. Better triggers + rumble. Motion controlled I guess.
Project Morpheus would be a priority too. I think VR is gonna be huge so I'd R&D that to heck and hopefully get it out by mid-2015/before the Oculus Rift. And then have some killer apps ready for it.
First/Second party games
Honestly I would have delayed The Last of Us and have it released as a PS4 exclusive. Naughty Dog loves to start each generation with a new IP and The Last of Us would have been a perfect way for them to open up the PS4 generation.
Have Sanzuru or another developer (High Impact?) work on a Jak and Ratchet crossover. Support Insomniac's Sunset Overdrive. GO AFTER TITANFALL! This was a huge mistake on Sony's part. Sony just can't do FPS right. Killzone is a failed series, Resistance also. No matter how much Sony tries, they can't get it. What I would have done is launch the system with Killzone, but also grab Titanfall and have them release it November 2014 with a single player + more game modes. I think Titanfall has (had?) potential to be a new Gears of War/Halo in terms of popularity.
Gran Turismo 6 for PS4 instead. A Level 5 RPG. Try and form a new partnership with a WRPG developer (Obsidian for example), or have Guerilla Games and/or Sony Online create an exclusive WRPG for the PS4 to rival other WRPGs. WRPG is a huge genre now and PS would have a good exclusive.
New Sony Santa Monica IP. A new Syphon Filter. GET THE LAST GUARDIAN OUT! That'd be a priority! A new IP like Eight Days could be popular.
Third party games
Try to keep Metal Gear Solid V console exclusive, that'd be a priority. I would pay for it and even co-develop it to get it out by 2014. Final Fantasy XV was offered to be a Sony exclusive but Sony probably couldn't afford it, but I would've went for Kingdom Hearts III which may have been a possibility since Kingdom Hearts Remixes were exclusive to the PS3. MAYBE at most make Final Fantasy XV a timed exclusive if affordable.
Street Fighter V of course would be exclusive. Maybe have another third party exclusive deal with Capcom, like for Mega Man Legends 3 or an exclusive Resident Evil game (not necessarily a main series one). Then try to get an exclusive (console) Square Enix RPG - new series or not. Namco is already developing an exclusive Tales Of game. Persona 5 exclusive of course. Maybe work out a huge timed (console) exclusive with a western developer (Mass Effect 4? Star Wars KOTOR? Fallout 4? Something like that).
So imagine by the end of 2015 the exclusive list will be something like: Killzone: Shadow Fall, Knack, LBP3, Gran Turismo 6, DriveClub, Bloodborne, The Order, The Last of Us, Jak and Ratchet platformer (or just a separate J&D game, and a R&C game), Infamous: Second Son, Titanfall, Kingdom Hearts III, Metal Gear Solid V (console exclusive), a few JRPGs (Tales Of Zestiria, Persona 5, Square Enix RPG, Level 5 RPG like Ni No Kuni), Eight Days, The Last Guardian, Street Fighter V, timed exclusive western game, wow that system would be amazing. PS2 status right there but even better.
Non-Gamers
I'd also try to attract non-gamers. Have social games, tons of indies, and also dance/simulation/fitness games that are popular with the female and older demographic. Research shows that women prefer those type of games. Basically I'd release games to try and appeal to women and try to get some exclusive deals like with Frozen.
And that's not impossible. 33% of Nintendo 3DS owners are women, because it has games that appeal to them like Animal Crossing (56% female userbase), Fantasy Life, Tomadachi Life, Style Savvy, Disney Magical World, Nintendogs + Cats, etc. etc.
As I said, not make it a real focus but try and expand the demographics a little bit. Only around 10% of PS3 gamers were female, the goal would be to try and increase that to around 20-25%.
Other stuff
USB support for headphones
Custom themes
Tons more applications
Upload straight to YouTube
3D Blu-ray support
MP3, MKV, FLAC, CD support
Local media support like DLNA
More seamless PlayStation Store (it's confusing now) and UI
