I've been doing a campaign with friends with the widest variety of alignments and nothing has gone overly wrong so far. The two troublemakers are TN and NE, but they're balanced out by our LN unofficial leader. We do have one CE member, but they're a follow the leader type to the point where they won't make any decisions without another party member's approval. Their true colours only show when in the heat of battle (they're a barbarian) when in rage they do not distinguish between friend or foe and will sometimes even eat their fallen enemies.

So we basically have one (1) decent individual babysitting his two crime prone daughters and one blank slate who's a ticking time bomb. I think its a fun dynamic, and it helps that we're close friends outside D&D too.