Small problems can be related to any number of issues, incidents, or disagreements. What matters most is how we deal with them. Small problems can arise relating to household chores, parenting styles, habits, expectations, and even, what to have for dinner. Small problems can be avoided by establishing and maintaining positive communication with your partner at all times. Trusting one another enough that you can talk about any issue or situation is imperative, because many problems stem from poor communication. Basic communication, such as calling when you will be late coming home, remembering to put the toilet seat down for her, and conveying your own wishes and expectations, is the key to avoiding fights that stem from festering problems.
Small problems can be avoided by pick your battles. Not everything has to be confronted. Unless it really bothers you, let it go. Know when to fight and how to approach the topic. I believe that approach and tone are everything. It can be the difference between a quite discussion and a huge blow up.