2. Movement and Encumbrance: Throw out the classic editions' movement rules completely. Assign base speeds based on race as per 4e. Apply the 4e encumbrance/armor rules. Use the 4e rules for movement in combat (shifting, double moving, charging, etc).
3. Spellcasting: Spellcasters can move and cast spells on the same turn. Casting times are not used unless they take longer than a round. Spells cannot be interrupted (see below). Low-level healing and/or buff spells such as Cure Light Wounds and Bless become Minor actions. Estimate area bursts and blasts to the best of your ability using the 4e grid rules.
4. Individual Initiative: Using individual initiative rather than "side-based" initiative will have the single biggest effect on your game. While the DM might still want to play monsters on the same initiative (as is common in 4e), have the players each roll d20, adding any sort of applicable Dex bonus (could be a reaction bonus for example). Do not roll every round; just stick with what you rolled just as in 4e. Players (including spellcasters) do not have to declare actions at the beginning of a round. Spells cannot be interrupted, as the casting begins and ends on the spellcaster's own turn. Players can ready and delay as per 4e.
5. Multiple Attacks: Do not stagger multiple attacks as per older editions; multiple attacks all go off on an individual player's turn.
6. Surprise: Throw out the old surprise rules and wing it. You could try to apply a "passive perception" feel to the game by allowing Elves and Half-Elves a saving throw or something.
7. Opportunity Attacks: Use the 4e rules for OAs; adjacent creatures provoke OAs from making ranged attacks or casting non-"touch" spells.
8. Ranged Attacks: Allow for firing into melee as per 4e.
9. Death and Dying: Do not use negative hit points. At zero hit points, unless the body has been destroyed or is unrecoverable, allow for three death saves as per 4e. Allow for another player to administer a potion as a Standard action as per 4e. A DM might allow a Cleric or Druid the ability to stabilize the dying as a Standard action.
10. Durability: A 1st level 4e PC is a hell of a lot more durable than its AD&D counterpart. There are many reasons for this, but we are going to ignore all of them except one: hit points. Keep the hit dice the same but allow for max hp per level. Thus a level 6 MU will typically have 24 hit points.
11. Use Ascending AC: I personally love THACO, but even many OSR games use ascending AC.