I picked up Arkham Horror last summer, because I'm attracted to cooperative games and I was in a mood to splurge. Since then, we've played three or four times. Each time, the game has been decent, but I've had the feeling that it could be better.
Here are weaknesses I'd like to overcome:
Our last game lasted from about 7:30pm until after 1am. That was long enough that I was getting bored by the end, though others were engaged enough to lose track of time. The best fix for this would be to get more experience, so that we can play without pondering the rules so much.
Lack of drama
We haven't yet had a game in which we felt much uncertainty about the outcome. Most of our games have been fairly straightforward wins, with one loss that was inevitable for a long time. This might mean that we're doing something wrong, or it might mean that we haven't played enough to get into close games. But we've gotten lots of very close games of Pandemic, and I'd like for Arkham Horror to have similar white-knuckle potential.
One part of the issue is that once you seal a few gates in key locations and get some good equipment, the game ratchets down in difficulty. Compare this to Pandemic, where the infection rate increases as the game progresses, so even as you become more able to handle diseases, the diseases get harder to handle.
Uneven distribution of drama
When you do not have plenty of weaponry, it makes sense to specialize: you give most of your weaponry to one investigator to make him able to reliably kill monsters, and send him out to do the monster-killing to let others move freely. While this is good strategy, it's kind of boring for the other investigators. In our last game, Mike was just using his trust fund to buy things which he would then give to other players to use—an effective and useful tactic, but boring for him personally.
In the same vein, it often seems that the game ends with one player setting off through the last gate to seal that gate, while the other players are mostly twiddling their thumbs and waiting to see if that expedition is successful.
Little identification with characters
I'm not sure whether this is really a bug or not, but I don't feel any connection to my character while I'm playing; I just think of the character as a collection of statistics, without any sense of story there.
So, my Arkham Horror-playing friends: how have you overcome those issues? What play combinations do you find most satisfying?