Well sweeties, in my personal opinion the only way Sonic the Hedgehog's home console games can surpass his levels of mediocre adequacy is to get back to the basics.
Focus on gameplay and the level design.
That's the most important factor to save Sonic. The misconception of Sonic is all about speed is one of things hindering new Sonic games to reach their full potential.
Now for my personal things they need to do:
Get rid of all the "other characters".
Back in my day, it was just Sonic, Tails, Knuckles, Amy, and Dr. Robotnik/Eggman. (Yes I'm ignoring everybody from Knuckles Chaotic.)
Keep the story to the point; defeat Dr. Robotnik.
I don't need to know, or care what happens in between.
No voice acting.
Pretty please? =D
Fix the camera in 3D Sonic games.
Nuff said, sweeties.