Common Failings of Arkham Investigators
Arkham Horror is an immensely complex board game; the number of mistakes that can be deadly to an investigative team are almost impossible to fully list. There are some general pitfalls to avoid that will up the chances of success, however.
There Is No I in Team
Of all the Arkham Horror common mistakes, this one is the doozy: Never forget that you are part of a TEAM.
This is the most common mistake new players make. It's also the most understandable. The number of truly cooperative board games (all players on one team, no traitors) on the market can be easily counted on the fingers of two hands. The idea that there is no winning unless everyone wins, and sometimes to defeat the Great Old One a player might be called on to sacrifice themselves completely is not something most players are immediately comfortable with.
The keys to beating the game are team communication and the willingness to be only one part of a winning strategy. Arkham Horror is a game where no one player gets to be the rock star. Plan out turns as a team, since often one investigator can clear the way for another. Don't hoard items - it doesn't matter how cool it would be to have a flame thrower. It simply needs to go to the investigator who can utilize it best. Clue tokens cannot be traded; decide as a team who should be picking them up.
Many small decisions made as a team ultimately build the best chance at victory.
Unless something goes horribly wrong within the first couple of turns, Arkham Horror is a long game. Plan to be there for several hours. Have munchies and drinks. Don't be afraid to chat about non-game-related things while someone's dealing with their combat. But more to the point, the sheer length of the game is another factor that needs to be dealt with. Players need to plan ahead - and all of that planning needs to be done under the assumption that the team will have to fight the Great Old One.
Don't wait until the last minute to go shopping. Many elder gods have attacks that require investigators to discard items, spells, or clue tokens. Others require a stat check that gets progressively harder. The attack should never come as a surprise - the information is available from the instant the enemy is selected. From that point, investigators need to work together to hoard the necessary items. If the attack involves a stat check, an investigator can try to distribute money to their compatriots to allow them to buy more skills. As the elder god gets closer to waking, at least one investigator should also be tasked with securing blessings for as many people as possible. Ideally, blessings should first go to the investigators best equipped to deal damage and survive for several rounds against the elder god.
Don't wait to send someone in to the first gate. Leaving the first gate alone for more than a turn often puts the team behind on trying to close the gates. It's very difficult to catch up after that point.
Don't let the monsters build up. It's easy to ignore monsters, particularly when they're scary. However, letting the monsters build up does no one any favors. More than two or three monsters on the board means that a series of monster surges can easily send the terror level through the roof.
There are many others that could be added to the list, but for Arkham Horror common mistakes these are the most prevalent and the easiest to fix.