I'm curious if anyone has played a campaign all the way to 20th level AND kept on going. What did you do? Did you just keep things at 20th or did you use house rules for some kind of Epic or Mythic play?
As a side note, how did 5E hold up at high levels?
My main point of difference is I use the DMG to create high CR monsters and NPCs since there are quite a lack of them in the MM (except for Dragons and Fiends). This makes them much more appropriately challenges for a high level group. Stock MM stuff doesn't stand up to well.
High level combat feels as dangerous and exciting as low level combat using DMG created creatures, I can still kill a high level character in 2 hits if I get lucky on the rolls.
1. High level Characters have a lot of resources at their disposal and are able to trivialize the exploration pillar of the game. My group turned a month of underdark adventure into a few hours using wind walk , and they are very effective at scouting using divination magic and stuff like arcane eye.
Big lake with a Kraken? Wind walk over it. Burning city filled with an enemy army? Wind walk over it. Tough encounter? Throw up a wall of force then Wind Walk out of it. Replace with Teleport, Fly, or whatever other resource your party has available.
They can also take extreme measures to protect themselves, so without "cheating", it's hard to wrest the initiative (the term - not the game mechanic) from them when running a module that doesn't cater for that.
In short, expect your players to have a much easier time retaining the initiative and dictating the pace of the adventure.
3. NPC spell casters created with PHB rules don't hold up so well. ~100-150 hit points, concentration mechanics, and lack of good all day buffs means they can be killed round 1 in combat pretty easily.
5. Bards and Rogues can get very high passive perceptions - and ability checks in general. Don't expect to rely on anything that requires a perception check to remain hidden for long.
6. If you use magic items, attunement starts to become quite a constraint at higher levels. My group now is starting to have a few interesting items gather dust because of the attunement limit.
Also an aside - magic items aren't too scary at higher levels. The Paladin player in my group has a +3 Vorpal Greatsword (recently acquired and all rolled for randomly) and it's impact on play hasn't been profound.
Likewise - The Wizard has a Staff of Power and Wand of the Warmage +3 - so a total of +5 to his attack bonus. It makes him like scorching ray a little more, and his firebolts don't usually miss, but I wouldn't say its game breaking.
I'll have to give this a shot.
That's harsh.
Dimension door and fly were used a lot to close the distance for combat in our campaigns.
We noted this too. Caster alone in room dead quick. Very little danger.
You have any experience with high level rogues? How are they?
We wouldn't allow a wand and staff to stack. We look at them in the same fashion as weapons. We wouldn't allow the bonus for sword used in each hand to stack together for a single attack. Wand and sword serve the same general function. You aim them at something and cast using them as a targeting device for spells. Sure, you could argue RAW it can be done. I'm about 99% sure it is not intended. From a fictional standpoint, it's pretty strange to have a guy aim a staff and wand at the same time gaining the bonus from each for a single spell.
Since this is the first time I can recall D&D incorporating magic items that give a caster a bonus like martials get with weapons, I imagine they didn't think they would have to write they don't stack together. To me it was intuitive that a wand of the war mage and a staff of power was an either/or scenario similar to the choice made between +1 greatsword or a +2 vorpal greatsword.
Rogues at higher levels are not awesome in combat. I'd prefer a Bard over a Rogue most of the time. Rogues can do better multi-classing into Fighter or Barbarian. Much better in combat (seen a Barb/Rogur with uncanny dodge tank?) and still get pretty good skills. Scouting can be replaced as well by magic when you have enough resources to dedicate to it (high levels).
On the other hand Bards are so awesome.
Barb/rogue uncanny dodge sounds ridiculous. Since the Uncanny Dodge mechanic works differently than barbarian rage, they stack. That is just nasty. And Evasion with Rage too. Evasion works different than Damage Resistance. So you have a tank that takes a 1/4 damage once a round from an attack and 1/3 damage from dex-save damage if he misses his save. That is insane. Were you able to bring that character down?
Bards do look awesome. I've never been able to get into the whole sing-songy thing. It is so hard for me to imagine some guy singing or orating on the battlefield. I keep trying to come up with a bard concept I like, but it always looks a little goofy in my mind's eye. I can see the power of the bard. I was thinking of a valor bard archer that used animate objects to animate some of his arrows when he ended up in melee combat. I thought that would look pretty cool.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.