Having services virtualized into cloud does not take away nor decrease the need for service monitoring and management. Viceversa they are becoming even more important as cloud enviroments usually increase the ammount of external vendors operating around your infrastructure.
One way to tackle these challenges is to re-engineering of issue management. Escalation processes most propably need to be renewed and you need to clarify roles and responsibilities of your vendors to match new situation. Most important thing is to secure proper interaction between vendors.
Dependencies between systems can prove to be difficult to manage, if you are utilizing several different cloud and physical environments simultaneously. Network connectivity and traffic loads need to be carefully planned as traffic is not anymore staying with in one network. Vendor relation is also changing, if you are moving at the same time from single hosting partner into multivendor environment.
These challenges can be tackled with functioning integration solution and professional network design. You might be interested in possessing some of these capabilities inhouse also. On top of these services has to be categorized carefully based on their special requirements so that their locations (cloud vs traditional environment) can be decided based on good judgement.