Let's start on a positive note by complaining about things Blizzard intentionally or accidentally ruined, broke, or in some way made less good than they were before. This isn't a complete list, just things that stood out to me.
Lower Blackrock Spire: Unless Blizzard has broken the standard they set, which really would not surprise me, a few quests, and therefore opportunities are missing from LBRS. Warrosh: totally out of luck. Vaelstrasza: no more ring quest, no chance at all that he's going to be making an appearance in UBRS. Bijou appears to no longer give any quests. No more worg pup or spiderling? No more getting milked by a dwarf? None of these are essential, but they provided some tidbits of story and helped fill out the instance. I am not claiming that any of them had reasonable quest mechanics, and I'd definitely say that Bijou's belongings were too hard to find. Also, required quest aspects (mother's milk poison) should not be able to be cleansed.
Stratholme: I mentioned this earlier; the instance has been cut in two, possibly making one boss impossible to summon (within reasonable expectations for a PUG, in other words, don't come it here and claim "it's still possible if you have the entire group run to the other door before it resets" because that's hardly a reasonable expectation) and generally hurting the ability of players to explore a bit.
Scholomance: No longer an opportunity to participate in brotherly murder. Cannot get a new trinket for Caer Darrow.
Blackrock Depths: Too big and complex to be based on the standard "kill last boss and leave" model, so it can be hard to complete quests. Mole machines should be for corpse runs, not for skipping every single quest location. Prisoners don't seem to scream as loudly as they used to. No more Love Potion quest. Emperor no longer calls the Senate to his defense, meaning that groups skip clearing, losing valuable opportunities to be taunted by him.
Stratholme: The simple story update explains why nothing really changed without simply being a "they're undead, so they came back." Timmy no longer ambushes your healer after clearing Crusader Square. This might belong in the Bad Things section. Also the quest for him claims that we need to clear Crusader Square to get to him and clearly wasn't updated to reflect his new placement. It's a minor issue, affecting only the fringe minority who read quests. I suppose that belongs in the Bad Things section, but it fit the flow. There is no longer a strangely long delay between the skeleton zerg rush and the door opening.
Scholomance: "Do you have the key? No? Okay, let's duel and hope a Horde kills us near the door," fixed.
Upper Blackrock Spire: Is now a five man, meaning that people can actually queue for it without needing to leave the LFD system and can even get it as random. I was very glad to see that this instance was open to the average player again. Previously I was only able to run it because a random LBRS group didn't know the instance and ran the wrong way, a mistake which I didn't bother to correct. While I am a bit sad to see the only 10-man non-raid instance go, I must admit that it no longer had a function in the new regime.
Scarlet Monastery: Teleport function fixes issue with ridiculously long, linear trash runs respawning when we're trying to get out.
It is a lot harder to get runecloth these days, but a lot easier to get mageweave. The old instance structure was set up for level 60, heavily weighted toward 55+ instances. BRD, LBRS, UBRS, three wings of DM, Scholomance, and two wings of Stratholme added up to a whole lot of places to farm runecloth. It also added up to a whole lot of instances that got skipped on the way to Outland. Even if LFD hadn't excluded them, just the eventual XP gain would mean that players were bound to miss some of them. These have been shifted downward in level, making them more accessible in the leveling game, and pushing several out of the runecloth range.
Overall I'm fairly happy with the level changes. None have been made low level, which I think would have trivialized them, and while clearly none are the same as what they were at 60, they do retain some of their distinctive nature. Given that the level cap is no longer 60, I think Blizzard has done just about they best they could to make these relevant and commonly accessible again. As my Bad Things list shows, not everything is perfect, but even those are problems which could be fixed and are not caused by the level change.
I've not heard of much changing in Outland, but I'll see what I find. At level 59 with a moderately unattractive, but epic, crafted Robe of the Archmage, my mage has left behind Azeroth and ventured out into Outland. Time for a whole new type of boar to kill. Oh what the... seriously? No new spells until 68? Bad Things list, you have a first candidate!
4 hours ago