You can't avoid bad meetings, really. But by planning ahead, you can change the tone of the meeting before it starts. Know what's on the agenda, and consider how you are going to feel emotionally and intellectually about each agenda item.
What do you want to say about that issue? Does that problem even concern you? Sometimes emotionally charged meetings can be diffused when one side or the other admits they can live without this or they don't care much about that.
Knowing, in advance, what really matters to you gives you confidence going into the meeting, and keeps you from expending energy on one agenda item when another is more important to you. Ask, What have I got to lose? And then answer that question, yourself, before you go into the meeting.
Talking to co-workers in advance of the meeting can help. Find out what their hot buttons are; ask how they are thinking of addressing some of the issues. What do they have to lose? Getting these conversations out of the way in advance will help you understand where everyone is coming from as they enter the meeting.
Shouting matches can happen in offices of all sizes. They are a waste of everyone's time and the company's money. Managing the tempo and mood of the meeting is everyone's responsibility, and it only takes one person to diffuse a bad scene. The magic words are, "I don't want to fight." The key is to be genuine when you say it. You are not there to argue; you are there to discover the other person's perspective. The more frustrated you are, the more important it is to ask questions. There is common ground here somewhere; keep looking.
Last week, I left a meeting with someone important. The conversation was about money, which is a hot issue for almost everyone in work situations. I said, "I don't want to argue. I just want you to help me figure this out." At the end of the meeting, I remarked, with some disappointment, "We didn't resolve anything." My co-worker smiled and said, "No, but now we understand each other's perspective." Maybe that was the most important agenda item of all.