Some options (some possible repeats of what others say):
- Give out Action Points a little more often, so that they are used more often as well. An extra immediate action can do a lot of damage.
- Don't be stingy with bonuses to hit if the players do daring maneuvers. Often what causes a slog is the "swing-and-a-miss" issue. If the players use good tactics, then this won't be a problem (they'll be flanking most of the time). If they don't, then throw them a bone: give them a bonus for high ground, for any stunts they perform, etc.
- Don't make the badguys fear Opportunity Attacks. In 3e, many people had this belief that they needed to avoid AoOs like the frickin' plague (because they did need to in that system). But 4e's high HP enemies mean that OAs are kinda okay. Also, many powers rely on them being triggered (or are at least are most optimal then).
- Make the Bloodied condition also impose a -2 penalty to all Defenses.
- Ignore the "one daily magic item power per day" rule. Each item with a daily can only be used once daily, but you can use however many daily items per day as you've got. More Powers thrown around = more damage = faster fights. Badguys can use this, too, so it's not unbalanced.
- Use morale. If every badguy fights to the death, then yeah, you'll have some slogging fights. If some run away when their numbers are cut down by more than 50%, or they surrender, then fights will go faster (especially the fights that don't really matter as much). Bloodied is a great indicator of morale: if an enemy is Bloodied, they know that they are in trouble, so they might seek alternative ways to end the fight so they don't die, whether that be escape, surrender, suicide (the ol' cyanide capsule trick whilst yelling "You'll never get me to talk, do-gooder!"), or whatever.
I'd say those are among the least "rulesy" ways of changing things up. If you want more in-depth gamey ideas, then you have to look close at the ramifications. Stuff like playing with damage rolls (or static damage), increasing crit damage/likelihood, reducing enemy HP across the board, etc.
- It might sound like it would do the opposite, but you could always make certain enemies into "Hardy Minions." These guys are Bloodied on the first hit, dead on the second. Why is this a good idea for reducing slog? Well, if you don't like the "turn 'em into minions" idea because it's "unrealistic" or something (I really don't understand that argument at all), then turn them into Hardy Minions. They'll last a little longer, but still go down faster than other baddies.
BTW, why is the "turn 'em into minions" idea so reviled by some people? What's the difference between that and any other rule that makes enemies die faster? If you're trying to make combats go faster, wouldn't this serve the same purpose and have precedent within the rules?
Just curious.