I think we have to differentiate between two types of multitasking:
- Multitasking done by your resources
- Multitasking done by you, the project manager
Now when it comes to your resources, let's examine the following scenario: A resource is working on a very difficult task, and suddenly someone (maybe you or his functional manager), tells him to stop working on this project task, and work on something else urgently. Needless to say, it will take him some time to switch from one task to the other (he's not a computer after all), and then maybe more time to switch from the "urgent task" to his previous, project task. The switching process can take an hour or two. So, when that resource multitasked, he wasted some precious company time.
Another example would be the team lead, who's working on a task, and who's asked for help by one of his colleagues. The exact same thing will happen, and precious hours will be wasted (in this case, the situation is worse, as two people will be working on one task that was originally planned for only one person).
I think multitasking is a bad thing when it comes to team members, but I find it nearly impossible to avoid (there will always be urgent task, and there will always be people needing help).
As for the project manager, multitasking is one of the qualities that distinguish good project managers from bad project managers. The project manager has to multitask: He has to answer emails, while updating the project plan, while answering phone calls asking about the status reports, and, while having a resource in his office telling him that he has difficulty completing a task. All this and we haven't even mentioned that the project manager could be managing several projects at the same time. While the simultaneous tasks that project managers have are many, they are not difficult, thus the switching process shouldn't be neither hard nor lengthy.
I think as you go up the ladder, multitasking skills become more and more essential. I can't think of a single CEO who's doing only one thing at the same time. Can you?