The other users will get some kind of an access error when trying to claim a task that has already been claimed by someone else.

当某些用户尝试请求已被另一个用户请求的任务时，他们将收到某种访问错误消息。

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Data access error!

数据访问错误！

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Since Friday, users attempting to access those applications received either an error message or were reverted to Facebook's home screen.

WSJ: Facebook in Online Privacy Breach; Applications Transmitting Identifying Information

As a result, users began to experience error messages when attempting to access their downloadable content, indicating that the DLC was unauthorized.

FORBES: Dragon Age: Origins Owners Locked Out Due To DRM Failure

As noted by Joystiq, trying to access your cloud saves is resulting in a 0x807b0198 error for many, although other parts of XBL like streaming video services and multiplayer gaming profiles are unaffected.

ENGADGET: Xbox Live outage temporarily disconnecting cloud storage for some users (update: restored, free month of XBL)