How honest should I be at work if I don't like certain things?

If things you don't like are about the process, write down the flaws and also your ideas to improve the whole scenario. If the things you don't like have something to do with personal issues, the best you can do is to talk to this person in a friendly yet assertive way. Try to explain what's wrong and how this is affecting your job, maybe preventing your team to reach its goals. Remind that you're not attacking and the reason why you bring this up is to have a genuine face-to-face dialogue. You care, that's the point. Everyone will enjoy your try to make a better environment.