If the 13MP comes with a better lens that would be fantastic.
They need to offer a S4 mini that isn't a piece of crap like the S3 mini, to target the 4 - 4.3 inch market. Lots of people, especially women do not like the extremely oversized phones.
The most impressive part of the S3 was not the hardware but all the changes they made to usability and features. If they continue this with the S4 and do not rest on their laurels this can get into 50-100% sales increase over the S3.
Bigger screen size is not a problem they just need to make the bezel a lot smaller. I really don't mind if the home button is placed in the side like volume and power buttons as long as the area is replaced with screen estate. Now if only S4 will have a machined polycarbonate or metallic form factor.
I really hope an RGB screen makes it into the S4. I almost bought the S3, but the nasty plastic and green/blue whites prevented me from doing so. Likewise, the small storage of Android phones isn't very appealing. I'd rather have 32Gb as the starting point and either have it expandable or give options for larger internal capacities.
To make this perfect, they will need to have the following:
Quad-core processor with Snapdragon S4 Pro speeds or higher
2gb or more of RAM.
5" 1080p RGB display with a THIN BEZEL.
Physical dimensions no larger than current S3.
Higher quality optics, no necessarily more megapixels.
Faster, more reliable auto-focus.
Dedicated camera button.
sad that companies still run after big numbers :| an 8 mpx camera but with better light sensitivity is way better than 13 mpx but darker, even in DSLR you can see this ... the 6000$+ cameras have lower Mpx than 3000$ ones ... but having fewer pixels on the same sensor size means larger area for a pixel to get light this translates in better images in lower light situations ... so high mpx values doesn`t really means better.