Pros
They offer reasonable health benefits. Being a global company, you get the chance to work with teams from all over the world. Expatriate assignments used to be offered (at the moment halted due to economic conditions). Among the companies in the US automotive industry, they're doing better than most.
Cons
Continental leadership got too acquisition-happy. They bit off more than they can chew. The leaders who made the big Siemens VDO acquisition are gone now and guess who is in charge? Massive cultural mismatch, IT systems that don't talk to each other, and politics. Want to do everything the "German way", so they send a lot of German expats to become middle management in North America. These managers' assignments only last 1-2 years, so they don't make any real changes. Most decision making is centralized in Germany. They're preoccupied with survival at the moment due to the conditions in the US auto industry. Little R&D in N. America, instead focusing on re-use and cost cutting. Losing their technical edge very quickly. Being a matrix organization, each department has its own agenda and typically works against each other. Lots of bureaucracy and red tape. Middle management takes a lot of time to make decisions, and typically after decisions are made, someone else tries to steer the team in the opposite direction. A lot of time is spent in unproductive meetings.