Implementing a hybrid solution does have some disadvantages, namely:
Security: The hybrid solution is solely reliant on the provider to provide best practices in protecting your data from unauthorized access.
Provider dependency: Normally called vendor lock-in. This is when it becomes difficult to move your resources from one vendor to another. An example that could make it difficult would be the amount of data to transfer to another vendor.
Technical issues: Diagnosing and fault finding system errors that have components distributed across several networks.