Based on my experiences so far, I have some obstacles I got through that I haven't read about anywhere. Then again, I haven't read a whole lot on meditation.
1. People usually say not to think and to let thoughts come and go, but sometimes I find I have to use thought to address a thought and/or "pull out" a thought from its root to make it stop. If a certain type of thought frequently appears, sometimes relaxing and going back to the breath doesn't suffice to stop it, so I just have to inquire as to the origins of it and let my mind dig them up, then address them and move on.
For example, if I'm frequently analyzing a certain social situation, I just ask myself what the significance of it is and it usually comes up, or it comes up why it isn't significant and the breath becomes more interesting and the thought stops.
The key I've found for this process is to be patient and accepting. Sometimes the answer to a question about one of my frequent thought patterns comes attached to the question, and sometimes it takes a while to pop up. Sometimes I can't find an answer during the session and it pops up later.
Edit: Another thing to look out for is that the answer, or a question that automatically follows an answer may be too "quiet" to be totally understood. Obviously being frustrated takes you away from finding inner peace, so the thing to do is to just be blank because it will come back fuller and it's best not to expect a specific time or level of clarity for it.
2. What happens outside of meditation is just as important as what happens inside. Sometimes we need to think, and sometimes we don't. It's good to recognize when to think and not to think, which I'm not 100% certain on. It probably differs for different people. Trying to force mindfulness and clarity can be disastrous if the subconscious really needs to address something. In the best case, it can be pushed to the back where it will pop up later, but in the worst case, it will conflict with the attempt to be mindful.
In other words, going "oh no, I'm thinking!" can be bad because it prolongs or prevents addressing a thought that may be important.
3. Peace isn't the absence of interruption, but harmony. What happens happens, so don't expect a constant state. I used to stop because saliva got stuck in my throat, or because my cat would meow at me, but things eventually pass or are not nearly as bad as I felt like they were when I accept them.
4. Expect to feel more things about your own body that you didn't notice before. Let those come and go or address and accept them like thoughts.
5. When you are able to shut off thoughts and develop a greater clarity from getting a sense of which thought patterns are relevant and which ones are not, thoughts can become faster and more vivid. Also, when thinking less, thoughts develop a greater sense of novelty much in the same way things experienced through the senses are when they're not clouded by thoughts. This added novelty and clarity in the thoughts can make it easy to get lost in thoughts again. That goes back to finding when to think and not to think.