The security right 'CSR-Edit Other User - Full same queue' is needed to complete the tasks / save the CSR even though both the task and the CSR ownership belong to the same person performing the action.
All versions until 5.7.1 did not have an issue with this right.
It should be that the csr_lock_status is not updated when the CSR is first opened.
This issue has been introducted by defect Stat-871 in 5.7.2.
STATUS:
Issue is fixed in Stat 5.7.2HF-a
