Shiroe approves this message.

The Villain with Glasses can be a complete and utter dick if you harm his friends get on his bad side. In fact, Log Horizon seems to make a point of having people with glasses be able to be total dicks while smiling.
The smiles. The smiles! 
Also, since I suppose a few caveats are due-
Log Horizon obviously isn't perfect. It doesn't have anything I would consider as a major flaw, but it does have... if not major weaknesses, at least things that could be better. Here's my personal top three.
Visuals: Modest with a use of recycling
Log Horizon is not a tier one anime in terms of fight scenes. Where some anime take pride in crisp, detailed art styles in which ever action is well choreographed and every fight visually unique and high-quality choreography and detail (tier 1 examples being Ghost in the Shell, Samurai Champloo, FMA, even SAO), Log Horizon is most emphathetically not. The art style is colorful and smooth and makes a point of avoiding character portrait details- and makes a point of keeping it that way. It's part of the aesthetic style, but the only crisp and detailed images you're likely to see are background images. Fights also occassionally make use of the dreaded clip recycle for re-use of abilities and other segments- it's modest, but there. So is the use of CGI of the monsters (but which is mainly only used for mass-monster groups). Just a heads up.
Plot: Sometimes flippant about Serious Buisness
It's already been pointed out that Log Horizon is sometimes called the 'happier' SAO. Sometimes this is because it moves past real and obvious spots of tension without giving it the sort of attention it might merit. A prime example is that while the issue of 'trapped in a game' is brought up, none of the main cast give it much weight- no one desperatly wants to return home, and there's virtually no thought about trying to seek out a way to return. Angst and sorrow for those left behind is for chumps and the rabble. This fits the narrative's theme of 'learning to adapt to living within the game,' but also creates a sense of lack of tension or development of the 'original side.' Everyone more or less has their strongest connections and reasons in-game, and the largest grievance about the outside-world is that some friends weren't online to be trapped. There are a few more, spoilery, developments that don't get the weight I think they might, but this is how it is. Log Horizon picks which problems it wants to focus on, and that means there are some that it does not.
Characters: Few strong, independent, leading females
This one is more of a (modest) pet peave than a huge issue, and certainly not a flaw to the degree that many other anime (including SAO) are. It just annoys me that, for how many things it does right, female characters are under-represented.
Take this image of the regional whose-who of players. These are the primary leaders of the people in the setting. Count the number of women at the table, and then subtract one because the one on the right is just a very pretty boy. (No real spoilers- just a picture of a table with people sitting at it.)
Yeah, kind of underwhelming, isn't it? The vast majority of the primary cast is male, and most of the secondary cast is male as well. Women are mostly in subordinate/support relationships. Truth in fiction, of MMO settings or real world convention? Perhaps, but annoying none the less- and especially for all the other things that Log Horizon gets right.
This annoys me, and to an usual degree, because how Log Horizon treats female characters is otherwise pretty strong. It passes the bechdel test, in which females talk to eachother and are able to have conversations that aren't about men. It repeatedly emphasizes that level, not gender, is the primary form of strength and weakness (such as when both males and females are targetted and even enslaved), and women are just as capable on the battlefield or in the boardroom. It doesn't define it's female cast by their romantic relationships to men (even the ones who are crushing have outside interests and context), it doesn't pile on a harem scenario, it doesn't treat them primarily as fanservice. Even when romance and crushing do come into play, it isn't to the exclusion of other attributes and interests: in some cases, the (non-romantic) relationship with a man is simply a character development catalyst for self-improvement and maturation.
So, yeah, compared to all that it may not be a 'flaw' as such... but it annoys me just a tad.