I must say, I was hesitant to watch the second season after seeing the first. The first season was a great idea, but the execution of it (the flow) was terrible. However, I decided that I wanted to know what happened, and if some plot holes were filled, so I watched.
I wasn't disappointed.
In fact, it's going to be hard to be objective in my review for two reasons. The first is that I have personal experience with dealing with a trauma (an issue brought up in the first arc), and that...well, to try and keep spoilers out as well, let's just say that I had a friend in a similar position (minus all the technology, of course) as a character in the third arc.
Moving on, I'll try to be as objective as possible. My rating on the overall story at the bottom will be the average of each story arc (which I'll put a rating to under the "Story" headline in this review).
Story
There are three arcs, all of which with different plots.
The first arc goes from episode one to episode 14. There have been two mysterious deaths in the real world, linked to a character in a new VMMORPG called "Gun Gale Online". The character, known as Death Gun, supposedly kills his victims in real life by shooting them with a gun in the game; a feat which shouldn't be possible by all the rules and new dive devices used after the disaster of SAO.
Kirito is recruited (and paid) to convert his character and enter GGO in order to help with the investigation due to his help with the investigators of SAO. This also brings a flash from the past, as he winds up dealing with one of the other SAO survivors.
(I'd give this storyline a 7/10)
The second arc occurs in ALO. There's a short mini-plot of the main group attempting to get the Excalibur and running into Gods of the world based off of Norse mythology; this arc spans episodes 15-17.
(This storyline only deserves a 2/10 for possible but wasted potential)
The final arc goes from episode 18 until the final episode of 24, and features a guild in ALO called the Sleeping Knights. It starts off when the main protagonists hear about a great sword fighter who duels with others, nicknamed "Zekken" due to her skills and having an original sword skill offered should someone wins.
Asuna is the last of the group to duel Zekken, who turns out to be a girl named Yuuki, and due to her performance in the duel, is asked by Yuuki to help the Sleeping Knights defeat a boss so that they can get their names on the Swordsman Stone in the village.
There's a sub-plot which occurs during episodes 18-24, which includes a little of the struggles Asuna goes through in the real world with her mother, as well as delving into Yuuki's character.
(Probably the best storyline; I'd give it a 10/10)
Characters
Putting aside the characters we already know from the first season, we're introduced to a few in the second season. I'm only going to list the protagonist characters to avoid possible spoilers (due to the fact that the first arc follows in a mystery-genre pattern, listing every character would be spoiler-heavy; I figured out "who" and "how" without any spoilers or knowing the character names beforehand, so just having a summary of the antagonists might even be too much).
There are two major characters introduced in the two arcs (not including the "interlude" arc for the Excalibur):
Shino Asada, aka "Shinon", is a new protagonist introduced in the first arc/the GGO arc. She's a sniper in the steampunk world of GGO who has a fear of guns outside the game due to a traumatic experience involving a bank robbery when she was 11 years old. In the game, that fear doesn't seem to manifest, and she's the one whom Kirito first discovers and asks for help from; granted, she thought Kirito was a girl at first, but she still helps him out. She's typically shy and introverted, but has a quiet confidence about her inside GGO.
Yuuki Kinno, also nicknamed "Zekken", appears in the next major arc which starts at episode 18 in ALO. She's a cheerful, upbeat, and accomplished one-handed sword wielder despite what she's going through in the real world. She's the leader of the guild Sleeping Knights, and is first seen accepting challenges from other players to duel.
Yuuki is also one of the few female characters introduced in the anime who does NOT fall in love with Kirito (a nice change).
Overall
This season, by far, was the best season in pacing and story. If the first season had this sort of pacing for the first arc, then I would have given it a much higher rating. Everything moved smoothly, and transitioned perfectly.
Yes, the first couple episodes (GGO arc) are a little on the dull side since they don't include Kirito or the others as much, and not all of it is even necessary to the story. There are also some plot points and issues which should have been addressed in the first season/anime rather than this one.
The first arc was interesting, and will certainly appeal to mystery lovers, but isn't exactly resolved. It has a conclusion, but not a complete resolution; something which costs the season some points. The motives are also a little vague, which cost it at the conclusion.
Now, the first arc was certainly interesting; between Shinon's trauma and Kirito having to confront a past SAO survivor, plus the overall mystery and fights, there's plenty to give the first arc a lot of points. It would have been perfect had all plot points been resolved.
There's also the mini-arc for the Excalibur, which ends on an odd note (with one NPC boss saying something strange), and really has no other impact on the overall story at all. Nothing more develops from it despite the interesting setup it was given, and such a thing really can't be overlooked.
The third arc is really what breathes life into the season. Perhaps some people might find it strange, or odd...and I'd probably put it on an emotional level of Clannad...but it was done perfectly.
The flow, the story, and the emotions were all great. I really can't go too far into it without spoiling it, and perhaps it won't impact someone who hasn't seen that sort of thing in an MMO community or had something similar happen to a friend (or family member).
There aren't many, if any, faults in the final arc with the exception of a passing mention of someone at the end and no elaboration on it. Everything else, from the characters to the story, was incredible.
For all the arcs, it would have been awesome if we saw more of the relationship between Kirito and Asuna, rather than the feeling that the writers couldn't quite decide whether to have it be a harem or not, but otherwise, not bad.
All in all, despite the GGO arc not having a true resolution (though it has a conclusion) and the Excalibur arc having a lot more potential than what was done, the second season was more enjoyable and suspenseful than the first season.