The gist of the Ashley/Mike fight is that they seemed to be really tight early on in the episode, and even went to church together, but Ashley feels Mike sides with a guy she believes is heckling her at a bar. So there's tension and fighting back and forth. Ashley randomly brings things up in their fight that have nothing to do with the fight, such as claiming Mike doesn't know who he is, that he's uncomfortable with his sexuality, and that he sided with the heckler because he's a guy and Ashley's a girl. The fight continues when the roommates are hanging out, and then when Ashley tries to prevent a girl from taking pictures of drunk Andrew at a bar. I swear, I watched this entire episode and I'm at a loss as to why this fighting continued throughout the entire episode, because I don't understand any point that Ashley was trying to make. Anyway, at some point they kind of make up and are friends again.
But I want to back up for a minute, to when Ashley and Mike's fight started, because this is the first time "Real World" has really acknowledged D.C. residents in the show. The fight started because the cast went to a Dupont Circle bar, and while they were eating, some drunk guys started yelling, "Where's Carson Daly? Are you Carson Daly?" I actually said out loud to myself that I hoped I knew the guys who started that. Ashley made a rude comment to the guys, but Mike observes that this is D.C., the cast members are just visitors, so it wouldn't kill the cast to be friendly with the locals.