"How much negative news about your current employer affects your ability to move laterally? For example, I was in-house at British petroleum during the Gulf oil spill. Would it negatively bias an employer?"
No. So the fact that you were in-house during something negative like that, British petroleum during the Gulf oil spill, I don't think that's going to negatively bias an employer. I don't think that's something to worry about. It would also potentially show a reason for you leaving or not working there anymore. I really wouldn't worry too much about that at all. I don't know that you want to leave that on your resume in terms of having anything negative on there. But at the same time, there's nothing negative about that on your resume.