Pros
Great place to live if you love the outdoors. Very interesting work, get to see the entire shipbuilding process from design to final product. Lots of opportunities to move around within the company and see a wide variety of parts to the business. Very friendly place to work, everyone is very open and willing to help out. Mainers are a great group to work with, a very unique (in a good way) culture. Don't let my negative comments below sway you away, there are a lot of great things about BIW that make it a great place to work, if you can accept a few minor problems.
Cons
For and engineer, #1 worst thing about working there is the unions, particularly the draftsman's union. Union contracts dictate that only union members (who are not engineers) can work with CAD. This makes it very very difficult to work there as an engineer. Think of writing notes on paper and handing it to a modeler so he can put it in CAD... The manufacturing union also has a stranglehold on the company, with very strict roles for each trade within the shipyard, often limiting what salaried employees can get done and slowing down progress in general. Very isolated in Maine, one of very few engineering job opportunities in Maine. Not much chance of advancement in General Dynamics beyond Bath Iron Works. Intern program is a little slim at the moment but is definitely working towards being a full fledged program. If working with manufacturing, often very difficult to get people on board for change. The manufacturing workforce there is aging and sometimes very resistant to change.