I made this kind of mistake too. What I learned is to be patient and double think about what I'm going to say before speak out. Also I've stopped to make much comments in group meetings. Instead, I talk to people in their offices if I have some question. Although I don't like this kind of communication, I have to follow the culture in our group while trying to change the culture.

About company politics, it's really difficult for us who are in the lowest level of a company to get the information. It helps me to have lunch with managers or directors from other groups and I've tried to read the company news and people's arguments in big meetings. But I still feel lost sometimes. Now I just told myself to be patient and only speak if no one or every one has said something