Log Horizon's weakest part is Minori's plotline
The most recent Log Horizon 2 episode has made me fully realize that the show's largest single flaw is how it's addressing Minori's romantic feelings for Shiroe, and unfortunately this is a serious flaw that significantly lessens the show for me; it actively makes things painful any time the storyline comes up. That the show focused almost all of episode 13 on the whole mess made the episode kind of unpleasant to watch.
The problem is not Minori's feelings as such; they're sort of vaguely realistic and if it wanted to, the show could do a decent plot handling the issues involved there in her mixture of hero worship and a crush. The problem is that the show insists on taking the situation seriously, with characters (starting with Akatsuki but not limited to her) taking Minori's would be romance as a realistic possibility. Various people clearly see what is going on, indulge Minori, and appear to see nothing wrong with the whole situation, when by all rights they should be either backing away quietly or taking her aside and saying 'um, look, you are 14 and he is a college graduate, no'.
In short, any actual materialization of Minori's intended romance would be deeply creepy and that the show strings along the possibility of this is itself not a comfortable thing. It doesn't help that this is a not particularly attractive anime cliche and/or trope in general, one that shows almost never handle well. As it is the whole thing feels very 'light novel', which is not praise.
The whole show would be much better off if it lost Minori's feelings down a well and then never referred to them again. I'm not particularly fond of Akatsuki's angst in general, but removing Minori as a nominal romantic rival and shifting things purely to gaining the courage to approach Shiroe would help a great deal (although not completely, since that particular trope is very shopworn).