As Managers and Co-Workers, we have all been in the situation of "It's not my fault, it's his/her's". Working within the blame game does not get results or resolutions for the need of the business. Many times I have heard, how do we make it go away?
Listen. Sometimes what is being said is the real roadblock to resolution and or expected results. Sometimes there is another person responsible for the business issue. After being an active listener, ask the right questions and remember that the expected end result is getting a resolution and supporting business success.
Coach. Generally the person who is the "blamer" will have a negative opinion about pretty much everything. If you are a manager to this person, take the time to coach the employee into seeing different perspectives. Encourage the person to gather information before providing feedback on the outcome. If you are a co-worker, as hard as it is, ask the person how they would have done it differently and engage in a conversation that helps the co-worker see the bigger picture. Remind always what the business needs are and use words like "our", "we", "us" to emphasis that there is more than one person in the equation. Example "Jim, I know you feel this is my fault however, our goal here was to present on time. Can we discuss how we would want to work through this project differently next time to reach our goals?" Keep the communication focused on the team and or business need.
Details. Keeping detailed notes such as emails and documents that support the final result are best to keep around so they can be referred to in a time of confusion and or unclear conflict. We don't do this to throw someone under a bus but to simply help solidify and remind of the initial expectations, agreed upon tasks and overall responsibilities assigned. Keeping detailed agenda's and minutes of meetings out in front will also keep everyone in the know and on task as well.