I've posted about what I'd do with a new edition before, but here it is:
Products
I would structure the product line around a single core rulebook/starter set, with three 'circles' of supplements.
The core rulebook would be a single book of no more than 250 pages, at a reasonable text size. This would include all the rules required to play the game, although it would of necessity include only a limited set of options. (Most likely, it would include four core races, four core classes, and only part of the level range.)
Core Product
On day 1, the big flagship product would be a big boxed set game, entitled simply "Dungeons & Dragons". The box would be aimed primarily at new players, would include everything required to play, and would be designed to get people up and playing quickly. So, it would include the Core Rulebook, a Quick-start Guide, an Adventure Book, pregenerated characters, dice, miniatures, spell templates, character sheets, dungeon tiles... heck, it should probably include a pack of pencils!
At the same time, I would make the Core Rulebook available separately, primarily for established players who want to get the new rules, but don't necessarily want to pay for all the 'fiddly bits'.
Key point: It would be the same Core Rulebook in each case. That way, the boxed set should retain its value when players graduate to the 'real' game - they're using the same rules, and they're using the same rulebook.
Expansions to the Core Product
I would be very tempted to put out an annual (or perhaps less frequent) expansion to the Boxed Set version of the game. This would include a new Adventure Book, more dungeon tiles, more miniatures, new pregenerated characters, and a bunch of other goodies. This would be intended for people who like the game as it is, don't want to deal with the hassle of graduating to the 'real' game, but just want more.
Circle One Supplements
Soon after the release of the core products, I would release my first circle of supplements. This would consist of somewhere between 2 and 6 hardback books that put back the 'missing' elements of the core. So, it is here that the remaining PC races and classes would be added, the rest of the level range would be covered, and so on and so forth. These books would be designed so that they form an interlocking set: you can use them with the Core Rulebook alone, but it is assumed that most people will use all of them or none of them.
Likely titles: Advanced Players Handbook, Advanced Dungeon Masters Guide, Grimoire, Tome of Treasures, Bestiary (possibly 2 volumes).
Key point: These books are supplements to the Core Rulebook, not replacements. So, character creation will only be in the Core Rulebook, monsters won't be reprinted, and so on. Again, this is about ensuring the boxed set retains its value - when people graduate to the 'real' game, we don't want them to feel they've wasted the money spent so far.
Circle Two Supplements
These are the supplements we're currently used to, such as the splatbooks for the various races and classes, DM aides, and so forth. Essentially, everything that isn't setting-specific would be here.
With Circle Two supplements, the assumption would be that you're using the Circle One supplements, but no other Circle Two supplements. While you may be able to use parts of the new "Complete Guide to Fighters" with just the Core Rulebook, the book will be written assuming you aren't doing this.
Circle Three Supplements
This would be everything setting-specific. It would also include pre-generated adventures.
With Circle Three supplements, the assumption will generally be that you're using the Circle One supplements only. However, they may occasionally use or build on material from Circle Two - but they shouldn't rely heavily on them. (c.f. the use of Psionics in 3e Eberron - it's mentioned, but far from essential.)
The DDI
This would include elements that tie in to all three circles. Because the DDI gives you access to so much, I don't think there's any great harm in tying it in to all levels. (There may be scope for allowing users to indicate which books they have, or even just if they're using the Core Rulebook alone or the full set of Circle One supplements.)
The Rules
Levels
I would bring back (but rename) the tiers from BECM D&D, including the Beginner tier that is missing from 4e (but not the ultra-fragile low-level PCs; 4e was right to eliminate those).
Beginner tier (1-3): At this level, characters would have an essentially fixed set of powers determined by class. There would be few fiddly choices for players to make at this level - the goal would be to get them playing quickly, and add complexity later.
Expert tier (4-14): At this level, characters rapidly gain in power. Players would have many more options for customising their characters, including multiclassing. The emphasis of play would be on the character's exploits - he's a hero in his own right.
Comander tier (15-25): At this level, characters reach the upper levels of their ability, and gain power much more slowly. The emphasis of the game would be on the characters being inspirational figures, leading armies, training apprentices, and taming the wilderness.
Master tier (26-36): At this level, characters continue to gain personal power slowly. The emphasis of the game is on building a legacy: characters rule nations, plumb the mysteries of the universe, and other similarly epic things.
The game would include advice for starting the campaign at the lowest level in each tier (for those who want to skip Beginner play, for example). Advice would also be given for adding 'back' the missing customisation options for Beginner characters (this would be aimed at more advanced players, though - the default would be to not have it, for the benefit of new players).
The Core Rulebook would include only the first two tiers: Beginner and Expert. Rules for Commander and Master play would be deferred until later.
Ability Scores
I would be inclined to go with a 4d6-drop-lowest in order method to create characters by default. I would also be inclined to reduce the importance of ability scores - +1 per 3 points rather than +1 per 2 as in 3e and 4e.
Temporary effects that adjust ability scores would be eliminated; permanent effects that adjust ability scores would be made much more rare.
Races and Classes
I would include only the Human, Dwarf, Elf and Halfling races and the Cleric, Fighter, Rogue and Wizard in the Core Rulebook. Obviously, for the 'real' game, I see no reason to limit the available classes or races.
Structurally, I would have each race give a small number of innate abilities (perhaps Elves get +2 perception for their keen eyesight, for example), and also access to a racial talent tree (to allow later customisation).
Each class would grant access to three talent trees (probably one per level in the Beginner tier, with the order being 'fixed' by default). Each class would also provide a list of bonus feats available to characters of that class.
Customising Characters
Characters are customised by two means: feats and talents.
Characters gain a feat at every even-numbered level (meaning that the first one is gained at 2nd level, sparing a new player from studying a big list of options before playing for the first time).
Characters gain a talent at every level, chosen from any of the trees to which they have access. Characters gain access to trees due to race, class, and (optionally) alignment(s). Additionally, there would be a feat granting access to a new talent of the player's choice. (There would also be 'prestige trees', available only to higher-level characters. These would replace the 3e "Prestige Classes".) When the character increases in level, the player may select a new talent from any of the trees to which he has access, regardless of what class he has just gained the level in.
However, a player may opt to take a bonus feat instead of a talent. This feat must be selected from the list of bonus feats for the class he has just gained a level in.
(Multiclassing is quite simple in this system: when the character gains the first level in a new class, he gains access to all of the trees for that class. Thereafter, he may buy talents from those trees normally.)
Skills
Skills basically work as in Pathfinder: Each class has a set of class skills, and grants a number of ranks. Characters can have a number of ranks in any skill equal to their level (with a cap of 15 in any case), and if they have any ranks in a class skill, they get a +3 bonus on the skill.
The skill list would also be essentially that of Pathfinder, except for the introduction of an Athletics skill (combining Climb, Swim and Fly, but also the Jump function of Acrobatics, and Run), and a "Ride/Drive" skill (covering Ride, but also things like driving chariots, controlling ships, and so on).
A Skill Challenge mechanic would be put in place.
Combat
The combat system would be more or less as in 3e. The Combat Maneuver Bonus/Defense mechanic from Pathfinder would be used. However, I am strongly inclined to de-emphasise the grid.
The 'real' version of the game would add a robust Stunting mechanic, to try to add a bit more flavour to combat.
Multiple attacks (both from high BAB and other sources) would be gone. Instead, characters would get extra dice of damage in their pool, and would be able to assign that damage to a target or targets as they wish (splitting would be less efficient).
Encounter Design
This would be done essentially as in 4e, including the Minion/'normal'/Elite/Solo split. Everything should be balanced on a per-encounter basis.
Other
Trivial modifiers, especially trivial conditional modifiers would be eliminated. The number of 'named' bonus types would be sharply reduced. The number of exceptions in the rules would be cut right back.