Like I tell people in real life: roll everything at once.
Roll attack and damage at the same time, it cuts rolling in half.
Luckily in 4E you don't have to ask players for saving throws on an enemy's turn, their defenses are static.
Also, play it no take backs style. You forgot to roll your saving throw? Too bad, you wait til next round.
Resolve Op attacks ahead of time. If the Fighter has somebody marked and there's a good chance that the mark will provoke an attack, have the Fighter roll an extra attack/damage roll at the end of his post. He doesn't need it? No harm. He does, you don't have to waste time waiting for him to post.
Each player's post should be their whole turn:
Start Turn.
Start with effects and ongoing damage.
Standard, Move, Minor, add Fluff as needed.
Roll saving throws.
End Turn.
Do not let your players break up their actions on a given turn between multipule posts. Make them ask all questions before they declare actions and then they must put all their actions in a single post. If they ready an action, they should roll it in the post where they ready it to save time for later (again, if their ready doesn't trigger, no harm done).
