I rarely get a feeling of grind in my games. Part of it is because of a houserule that encourages my players to use dailies (they get to recharge a daily attack power every milestone). Mostly it is because the players are tactically savvy. Some basic tricks they use often:
1)Never use a limited resource without a tactical advantage unless it is reliable. In a two-leader group with a battlepriest and a tactical warlord, players often request (in game, while roleplaying) some form of attack bonus before using a limited resource. This is the big reason why the relation between accuracy and average damage is complex: a miss by a daily is far more problematic than one by an at-will. However a miss by a daily only seems to happen rarely if you pay attention.
2) Make sure you have attacks available against different defenses. Get your hands on a foestone ASAP. Knowing where you can hit a monster hard and being able to hit there is critically important. Some classes admittedly have mainly AC/Reflex to hit, but there is often some Will or Fort attack hidden somewhere as well. Find it.
3) When a monster is about to get bloodied, ready actions to gang it! Bloodied Elites usually get very dangerous. Some can heal, others just do more damage than your defender's healing surge value. When a monster gets angry, kill it fast. 3+ Dailies hitting (especially if two are from strikers) can kill most bloodied elites.
As a DM I do the following to decrease the feeling of grind.
1) You don't need Intimidate to intimidate. If the players bring the wrath of gods upon the mobs, the remaining minions may start running for it, the normals are likely to try to run for help, and the elites are likely to do the best they can to make sure the runner makes it. In most cases the PCs will not allow the runner to pass ofc, but the couple of runs of would-be grind that become a frantic chase are an improvement.. If all else fails some monsters may surrender and offer information in return for their lives.
2) 4E does not have to copy the bad features of WoW. The boss monster that waits for your players in the end of his lair and is hardly seen before is boring!. Especially a solo can feature in multiple encounters. His limited healing surges mean that if the players give chase, they may be depleted when they get to the final fight, but the solo will also be near bloodied or worse as well.
Now I could say more but I have to grab a cab
Bottomline is, grind, on most game systems is far more likely a result of bad gaming than a problem of the system.