Things I don't think 4e does well.
1. Novice characters. A fourth edition character starts out clearly distinct from the common town guards (not necessarily better as a glance at the monster manual town guard will tell you), but distinct. The mechanics do not help you create a sense that characters started off as ordinary people who took on an extraordinary task and by overcoming challenges ascended to the top of the world. Instead, the mechanics get in the way of that. The PCs were never ordinary.
2. Skill challenges. By this, I refer to the rules for skill challenges in the DMG--either before or after errata. The mechanic for skill challenges is terrible and more often serves to gloss over story elements than to immerse players in them. I think after two years of play the, "DMs/authors just haven't figured out how to run/write good skill challenges" excuse has worn out. If the rules were any good, people would be using them well by now.
3. Non-combat encounters. Now, this has already generated some controversy in the thread. Obviously if you're the kind of DM or player who doesn't want rules to get in the way of your fun, then you're going to be fine with 4th edition's ability to do non-combat encounters. For players and DMs like me who like to have an idea of what our characters should be able to accomplish outside of combat, the rules for skill uses tend to be rolled into the rules for skill challenges where the DC for whatever you want to do is 5/10/15 +1/2 level. The end result is that you don't really know what you can do unless you are in a skill challenge (in which case, it's pretty much the same as it was at 1st level). And if you're not in a skill challenge, for a lot of things, you have no idea what the DC is or should be.
4. Rituals. Yeah, you can do them. But other than the cure disease/etc line of rituals, why would you? The basic scrying ritual, for instance takes a long time to perform, only gives you 30 seconds viewing time at best, and is so short range that you can probably see the location you're scrying anyway. If you want to outdo Iggwilv and bind Grazz't, rituals would seem like the perfect instrument, but there isn't a ritual for doing that. If you would like to make your castle fly, there's no ritual for that either. The system has just enough rules for curing that you can fix what monsters do to you and enough rules for divination that you can figure out it's never worthwhile. And it has rituals for things like waterbreathing that are needed to facilitate certain types of adventures. But it does not have rituals for anything that would drive the plot itself. Those are for NPCs and don't need rules.
5. Make combat quick. The proof is on this one. In LFR, it is quite frequent for convention organizers to extend the game slots for paragon tier adventures to six hours because otherwise there isn't enough time to finish the module. It's not role-playing that is taking all that extra time. Nor is it usually the case that they are trying to cram more combats into the modules than they were before. (In fact, LFR modules often have fewer combats than Living Greyhawk or Living Arcanis modules did).
6. Run mid-sized to large combats. If you don't like the minion rules, you're completely out of luck for running a combat with two enemies per PC. If you wanted to run a combat with three enemies per PC, you're probably out of luck even with minions. The xp per monster system and the relation of attack to defense and hit points in 4th edition means that you're pretty much running combats with 1-8 non-minions, tops and maybe up to 8 minions. But more than that and it stops working.
7. Run non-distinct combat encounters.
If you don't get a short rest in between two encounters, even two relatively easy encounters can threaten a TPK. You need that five minute rest and consequently kicking in the door and clearing out a whole dungeon in glorious round by round combat is out of the question. Likewise, "the guards sounded the alarm, and you hear the rush of booted hobgoblin feet that will probably arrive in two minutes" is a signal to retreat rather than to drink a few potions or move to defensive locations.
8. Run a sandbox campaign.
4e works if the DM is driving the campaign. If the players are doing so, it is much harder to make it work. The "whatever the plot requires" attitude towards the abilities of NPCs makes it impossible for PCs to engage in a game of preparation with distant NPCs. You can't keep non-detection up so that the NPCs don't scry you. (First, there isn't a non-detection ritual. Second, there aren't useful scrying rituals which means that if they do try, the DM has a new ritual that you don't know how to use or defend against). Likewise, you can't anticipate that the NPC will attempt to raise the soldiers who died in the last battle as undead and use them against you but will be limited as to how much he can raise because you stole his onyx gems last session. Since there are no rules for creating undead, you don't know what he needs or how many undead he can raise--ordinarily the answer is, whatever the plot demands and whatever makes a useful encounter. While those answers make sense in the context of a story-driven campaign where you have to stop the bad guy from getting the whatever it is he needs, they don't work in a sandbox campaign where you try to understand his capabilities and make plans to neutralize them.
9. Beginner characters.
Even the "stand 25 squares back and twin strike with my greatbow" character is far more complex to run than some characters in previous editions were. There are no longer super-complex characters like wizards were in previous editions, but there aren't simple ones like previous edition barbarians or fighters could be either.
I have to strongly disagree with 1, 2, 3, 4, 6 (especially), 7, 8 and 9.
1) 1st level characters may be distinct from the town guard (although a fighter more or less fulfills the same job) but as you mentioned they are not overwhelmingly more powerful- and we haven't even discussed orcs, who would at equal numbers present a serious (n+3) challenge to 1st level characters. Characters are more developed than their monster-level equivalent and have a few more tricks, but not so much that there is a severe disparity.
2) As a DM I've run a number of skill challenges that worked brilliantly. Skill challenges are an art and a difficult one to master- for a new DM they can end up being clunky and repeditive (my first ones were, certainly) but done right they are a solid mechanic and help to flesh out noncombat encounters. Furthermore, once the DM has the basics down pat they can be easily generated or amended on the fly, creating plenty of room for initiative and creativity.
3) Again, sorry but I have had little problem as a DM with adjudicating on the fly- especially since the handy DC 10/15/20+1/2 level rule means I have a good baseline to go on if someone wants to try to sneak around/talk their way out etc. As I mentioned before, the skill challenge system means that even complex plans can be easily ruled on. This is a huge step from 3rd edition, whereby the DM often had to rely on 1 or 2 skill checks to determine pivotal events (or worse, a saving throw against a magical duex ex machina).
4) Rituals have proven less useful than I would have hoped for- absolutely. Just not as useless as you make out to be. So far I've seen rituals used for all manner of player shenanigans, effectively opening up new pathways or options for them to overcome noncombat challenges.
5) I agree with this. I've reduced hp by a quarter across the board to compensate- this seems to work well.
6) My group of 7 (including two NPCs) finished last session defending the top of an abandoned watchtower against 40 gnolls, including 24 minions. The challenge level is high but not outside of the player's ability to deal with as per DMG guidelines. The monster stats all fall within the DMG stats, too. The sole rule I have broken is making 6 minions = to 1 monster, and this is based on playtesting rather than an attempt to beef up the numbers for number's sake. Other encounters included 80 zombies + 2 wights against the 5 PCs. Both encounters were/are being enjoyed by the party. Prior to 4th edition if you wanted a mass combat you would have to rely on low, low level monsters- monsters that, as the 4th edition rulebook noted, the party would easily just roll over with a handful of area effect spells. 4e represents the first (and in my campaign at least successful) attempt to address this.
My suggestion is to try to use monsters 1-3 levels lower than the party as mooks- you will be able to throw more at them, especially in regards to minions (also- use more minions. The DMG has overestimated their power- something it did wrong).
7) A string of encounters, one after the other, is out of the question, although it really depends on what your DM's view of an encounter is (I've had no problems with reducing it to 30 seconds or lengthening it to several hours to suit the situation or event). Two encounters at level equivalent however is not going to tax the party, however.
8) There is a non-detection ritual if the DM says there is- jot it down on the monster sheet. The undead summoning rules are whatever the Dm says they are- jot them down on the monster sheet. This is not cheating since the monster generation rules are entirely about the DM creating what he needs. If anything, the quick, easy encounter generation rules (I can easily create an 'orc encounter' list from levels n-3 to n+5 and keep it on hand if the players do something unexpected in the orc lands) and the quick, easy writeup of encounters suggested in the DMG means that sandboxing is far, far easier in 4e than in 3e.
9) I will agree that starter characters at high level are slightly easier in 3e. So long as you are willing to accept a handful of builds for a handful of character classes- beyond this you were screwed. Overall, 4e has reduced complexity across the board.