There are always two aspects to any project, the project management deliverables, plans, registers, risk, issues etc and then the actual project deliverables.
The project manager is responsible for the project management deliverables and the project team for the project deliverables. The PM who is generally not the subject matter expert has to rely on the expert advice of the project team. Having said that the PM needs to ensure that the project deliverables have been through the necessary quality checks and are signed off by the responsible parties.
Whilst a design document is an important component of the project deliverables it is no different to any other. So make sure it has been reviewed by the project team, it has been tested against the functional and non-functional business requirements i.e. it is going to deliver the goods, and that all the necessary areas have reviewed it, IT networks, open systems, etc. and don't forget that very few systems end up being built exactly as designed as unforseen "stuff" happens.
