I have yet to run the Adventure Path (real life keeps getting in the way) but it has been a very interesting read so far. The two things that I haven't liked too much so far are:
1. The time span
As someone mentioned earlier, the time between the first adventure and the last adventure seems to be very short. The Adventure Path takes players from 1st level through to 20th level. I don't know what everyone else thinks but I think that at least a few years if not more should pass before a 1st level character reaches 20th. Otherwise why aren't there hundreds of epic level characters running around? Sure a fair few would die along the way but the law of averages says that at least a few would make it.
2. The amount of dungeon crawls vs. wilderness adventures
This adventure path seemed to contain quite a few dungeon crawls but hardly any wilderness adventures. "The Test of the Smoking Eye" might be considered a wilderness adventure by some but I think that is more of a planar adventure than anything else. I think that the ranger misses out a bit in the Adventure Path because his wilderness abilities are not utilised for the majority of the adventures. The same can be said of the Paladin's mount, or any mounted character for that matter. A few more traditional wilderness treks would be nice.
As for what I would like to see in the next Adventure Path:
1. The use of more standard creatures. A few adventures where orcs, kobolds, gnolls, etc., I felt that a few of the creatures in the Adventure Path were used just to try and encourage people to buy the Fiend Folio.
2. Multiple plot threads. There was some seperate plot threads occuring in the Adventure Path but they seemed to be left hanging as the Adventure Path concentrated on the Shackleborn plot again. I'm not sure if this was on purpose so that DM's could close themselves or due to time and space constraints. Either way I would like to see a few more followed through to conclusion if possible.
3. More wilderness adventures. I think that it would break things up a little as well as giving classes like the Ranger their chance to shine.
4. More background. Give me more information to help me immerse my players in the adventure. The more I can tell them about the world, area, person, adventure, etc., the more they get into the adventure, roleplay more and so on.
From what I have written it may look like I didn't like the Adventure Path. This is far from the truth. I have loved it from the start and I'm sure the person who thought of it at Dungeon must have a sore back from all the pats on the back he or she has gotten (along with a healthy pay rise right ;-) ) I am only mentioning the things I liked/didn't like so that the next Adventure Path can be even better!
And despite what it looks like I am not a wilderness loving, ranger playing, 1st edition fanboy. I have only ever played 2E AD&D and 3/3.5E and my favourite character is the urban halfling rogue.