So 4e has this problem with combats devolving into long slogs of whittling away at colossal HP totals. There are a number of commonly-suggested improvements, but ultimately as a highly-tactical, rules-heavy game, combat is the emphasis of 4e and it tends to take quite a bit of time even when you do everything you can to limit that. In addition to these approaches, you may want to have some of your encounters intentionally be those that the group “shreds” just to indicate that an area is hostile without taking too much time.
Make sure everyone does their homework
4e does a pretty good job of giving everyone a variety of options—powers—to use in combat, and places a lot of emphasis on careful positioning. These factors contribute to turns taking a long time to make decisions.
So an obvious first-pass improvement is to make sure everyone is as familiar as possible with the options available to them and the various tactics that are useful to their character. Defenders should be looking to harry an opponent or protect an ally, controllers and leaders should be looking to keep away from strikers, strikers should be trying to take out enemy controllers, leaders, and strikers, etc. (These examples are heavily simplified and do not even apply to all classes in those roles, to say nothing of characters who have secondary roles.) Ideally, everyone should be able to look at a battle and quickly assess where they want to be, and what powers they have available that are useful.
This won’t fix all the problems, and hopefully combats, the important ones anyway, are throwing enough curveballs that players cannot just apply rote formulas, but it helps.
Avoid monsters from early on in 4e’s publication history
Monster Manual III has a well-deserved reputation for “fixing” monsters. Try to stick to monsters that are from the post-MM3 world. This does a lot to make the math work out better, trying to find the sweet spot between shred and slog.
Use parties of monsters as much as possible
The biggest problems in 4e are the solos; groups of monsters tend to just work better. They don’t need giant gobs of HP just to stay standing, since they can be spread out and overkill doesn’t help anyone. It also makes more variety in one’s powers useful.
When using solos, consider the Angry DM’s approach
The Angry DM is a blogger whose D&D Boss Fight (Part 2, Part 3, Part 4) article is one of the best I’ve seen on the subject (in any edition). There is some mild language/attitude (occasionally using self-censored expletives of the “#$%!” variety), so YMMV on how entertaining/grating that is to read, but the ideas are excellent.
In this article, he summarizes some key problems with solos:
Most Solos Do Not Act Often Enough
Solos Lump Most Of Their Actions Together
Solo Fights Are Static
Solos Are Disproportionately Affected By Conditions
Everything Cool Happens At The Beginning
There Is No Sense Of Progress
He also rejects a common reaction to these problems:
Of course, you can fix most of these problems just by speeding up the fight with reduced hit points and defenses or by increasing the solo’s output with attack and damage boosts, but I would argue that that is selling the system short. A long fight with a powerful monster is not, in itself, a problem, so long as that fight is fun and exciting from beginning to end.
His solution is “a boss fight in three acts,” using three entirely separate stat blocks to create a monster that changes as the fight goes on. You may recognize this approach: it’s been a classic boss fight trope in video games for decades. It allows for a sense of progress and it gives the monster new powers, so that new things happen that the players have to react to.
In fact, mechanically, the three stat blocks are tied to three separate creatures. The “death” of a stage triggers the creation of a new monster with the next stat block. This is important because a new monster doesn’t care at all about whatever was going on with the last one: all conditions are wiped away, overkill damage on the previous stage doesn’t matter, and so on. This is important because it limits the amount of problems caused by controlling conditions on the boss, and because it gives the players significant incentive to save some daily and encounter powers until later in the fight, rather than blowing them all as soon as they see an obvious “boss” monster.
He also details ways to change this up, for instance replacing the middle stage of a boss fight with a skill challenge (a chase scene; his articles on running those are also excellent).
Overall, a very good read.