...but in my short lived (1st-4th level) play experience, there would sometimes be a player who just could not sort out his powers and abilities in a timely manner.
I too have experienced this. I've seen people complaining about how their combat rounds (with a group of 5 players) take 15 minutes, and it boggles my mind. My group's combat rounds take about 6 minutes as a rule.
The key, to me, is to
do your math ahead of time. I don't use power cards any more - I tried them, but decided they were more trouble than they were worth, and I'd rather be able to fit my character onto a single sheet - but for every power I have, I write down the attack bonus and the total damage on my character sheet next to the power name. Saves a ton of time.
Beyond this, I find that combat grind occurs when there are no more meaningful choices to be made. As soon as that happens, the whole thing settles into a slog. Once the PCs run out of encounter and daily powers (or expend all the daily powers they're willing to use on this fight), the chances of grind go way up; it is then incumbent on the DM to either end the fight quickly - e.g., the monsters run away - or ensure that there continue to be meaningful choices after the ones built into the system have been exhausted.
Player strategy is a big part of this. 4E is clearly built on the assumption that people will look for the best possible moment to use their encounter and daily powers, even if that means using at-wills for a couple of rounds at the start of the fight. That stretches out the span of time during which there are meaningful choices to be made.
However, a lot of players burn all their encounter powers right away and then have nothing left to do for the rest of the battle. IMO, this is a failure of game design. Tactical mistakes should be punished with defeat, not boredom.
I'm coming to the conclusion that it was a mistake for WotC not to include some way of recharging encounter powers during a fight. IMO, that would do a lot to prevent grinding. (Maybe one standard action to recharge one encounter power?) Or else have some sort of power-up mechanic that keeps people from "going nova" with their encounter powers.