The link of data mentioned does exist, but only for LDS.org, not for one unit's MLS to another, nor for a unit's CDOL to another. LDS.org does not push information from one unit's MLS to another unit's MLS, nor from one unit's CDOL to another unit's CDOL. Some prior comments in this thread make it sound like entries in one unit's MLS or CDOL ("Show all assignments") are the result of another unit's MLS entries, which is not so. The only assignments at present that a unit will see in MLS or CDOL are those that have been entered in that unit's MLS or CDOL, while on LDS.org a home unit will see an assignment entered from another unit because the assignment was entered using a member's record number. For this reason, wards or branches need to stay on top of any out-of-unit callings (or active callings assigned to moved-out members that might be stuck in the system) and properly release the individuals in MLS when they have completed their service so that the current home unit is not carrying assignment discrepancies on the LDS.org site, over which the home unit has no control to change in MLS or CDOL.
While I can see the benefit of displaying this information on LDS.org, perhaps the communication between the website and the two feeding applications of MLS and CDOL should be reviewed to consider if one unit's failure to release individuals from callings in MLS should continue to affect the accuracy of the home unit's LDS.org callings list, besides the other unit's callings list. Actually, to me it doesn't seem that big of an issue, as the callings list for any given unit is only visible to a limited number of individuals (it's not like the issue is announced at general conference or broadcast in the media). The biggest issues are that it displays inaccurate information (and we always strive for accuracy) and that the inaccuracy is not controllable by half of the group it affects.
The possible edit tools for the callings list on LDS.org, mentioned by Ryan, may be just the ticket for resolving this issue.