I know the world needs another review of Dungeons and Dragons 4 like a hole in the head. But here are my thoughts on it. Please permit me to start by identifying my criticisms of the previous editions.
I thought the skill system was inadequate in Dungeons and Dragons up to version 3 and workable but very unnecessarily complicated in version 3/3.5 (In early editions, an Ogre who spent a few weeks working as a silversmith was more skilled than a brilliant human that studied for years. In 3/3.5, Intelligence covered skill points so if you wanted someone with great skill in climbing, jumping, swimming, and moving silently in the woods they also needed to be a member of Mensa).
I thought non-spellcasters were less powerful and more importantly much less interesting to play at high levels in previous editions (Why would the Thief sneak around when the Wizard can make people invisible? Why would the Fighter bother to learn a new language when a Cleric can cast "Comprehend Languages"? Why would the Barbarian fight when the Wizard can summon a Griffon to slaughter opponents better than he ever could? Why would the Bard use his silver tongue to get information when the Wizard can cast Telepathy spells? etc... )
As a related problem, non-spellcasters became increasingly dependent upon equipment. If your high level Fighter had his magic armor and sword taken away, hordes of foes that he used to mow through like a chainsaw are now impossibly deadly to him.
I disliked the organization of spellcasting. If your Wizard is only a master of cold magic, that's a superficial bit of game flavor. The rules let him toss fire, ice, acid, lightning, and sound shockwave attacks, teleport, fly, shapeshift, and manufacture magical items all with equal proficiency. I prefer organizing magic along conceptual lines where each kind of magic, like attacks, telekinesis, summoning creatures, shapeshifting, healing, divination, and so forth, are all distinct enough from each other that no normal mortal can master them all. If Wizards are magical engineers, then Dungeons and Dragons assumes a world class chemical engineer can switch jobs and design a next generation computer processor the following day, engineer a cure to AIDS the next, and then find a harder and more durable replacement for Titanium that costs $0.03 per pound on the day after that.
Ability scores are largely fixed. Conan, Beowulf, Galahad, Merlin, Gandalf, Aragorn... there was no way your PC could imitate those characters using typical game rules.