Boeing is so big. Don't be surprised if it seems like you're working for the government. Like any big company you have to get use to the beauracracy (sp?).
There's a lot of work in the 787. Almost every department seems to be in a rush to meet schedule. So you'll never run out of things to do. If you're looking to be very busy this is the right program to be in.
As for upward mobility, it's going to be hard if you come in as a worker bee. You're going to have to accept a lot of responsibilities to get noticed and higher visibility. And you just have to wait for an opening created by either somebody leaving the company or retiring. Your best bet is to get an MBA if you're going the route of management, though. Boeing does have pretty good education opportunities.
Don't expect a lot of rewards for showing excellence above your fellow man. Certainly not pay wise, but it does make your more visible and increase your chance of moving up. Don't expect to move up fast, though. As you stated "it is just a case of having to serve your time before you move up". IIRC, raises come every 6 months. I been a contractor for awhile now, so don't quote me on that. The mentality of contractors are a lot different than direct hires.
All the direct engineers all belong under one union, SPEA. They are not exactly known to be an agressive union. I can't really say anything good or bad about them.
So far at any place I worked, Boeing management has been friendly enough. The managers take a more hands off approach leaving the leads to deal with the worker bees directly. Even then none of the leads I've dealt with micromanage. As expected of stereotypical manager roles, the managers attend a lot of meetings, business travels, handle corporate policies and politics.
My one main gripe about Boeing (and this is probably true for any large organization) is that everyone is afraid of hurting each others feelings. If you do something wrong, heaven forbid if someone will tell you. Upfront criticism is very rare. They always try to find an indirect way to address it. This does provide somewhat a safehaven for the lazy, nonproductive workers as well as those who only want to take advantage of the system (ie disability).
The workplace is such a PC environment too so you have to be careful about any off-colored remarks. I've heard enough horror stories to avoid all beautiful women at work unless work related. Call me paranoid.