Material created in MM01 but showing locked in MM02
The problem could be that the update task is running very slowly, or stopped altogether.Remember that SAP updates don't really happen immediately, they are queued for update, although with everything working well this should be invisible.
If there is a problem, the update task can stop and so queue ALL updates behind it until someone resolves the problem.
Speak to your Basis people and ask them to the update task. (you can have a quick look by using SM13 and selecting "to be updated" this should be empty or nearly empty).
Material created in MM01 but showing locked in MM02