Influencing Behavior
This is the worst offender of the whole achievements system. As I previously stated, a game already has its own motivators -- in fact, the purpose of a game designer is balancing motivators around a goal to create the intended gameplay experience.
But some achievements actually influence players to act in ways that they would not normally act. I remember this kind of thing happening a lot in Team Fortress 2. Often there would be a medic doing something really stupid instead of healing teammates. Angrily, I'd ask, "What the hell are you doing, dude? Heal us."
"I'm going for an achievement", he'd reply.
This is really not that rare an occurrence, particularly when a game is new. We now have a situation where players are actively not playing correctly and disturbing or ruining the game experience for other players because of achievements.
A common mistake would be to blame this on that player. Let's put it this way: if you're blaming a player for wanting to make use of the system of achievements, then you're proving my point even further that they need to go.