IMHO the biggest problem in project management is overselling the client by not only the engineers but also contactors and suppliers. The client gets an idea that he can have time,budget and quality in the same package. When the reality sets in then the lawyers get called. It is very important to know and understand what your engineers do and also which contractual consequences engineering decisions may have. If you do this you will have nice calm sleep in the night, the job will be satisfactory for your client and it will not be the last one for your company.
Contracts always seem to have ambiguities which are exploited by hard nosed clients.
Who does what is the commonest problem. We argue of course but the tension created does not help co-operative relations. I haven't been fortunate enough to work on a partnering project. The most basic problem in Project Management during the design stage is the contractual definition of work for the design engineers, I know sometimes the design engineers works under the blanket of the architect but if the design engineers has his own contract for the design it is not well define as the contract for the Contractor who will be doing the construction of the design. If we first define the reality of the complexity of the design process to the client by defining it within the legality of the contract documents maybe the client will understand the whole process which cannot be done overnight.