Parse is built to be scalable, so the most likely obstacle you face will be designing your data model. If you have a SQL background (or if you build your backend in SQL), your backend will be more likely to suffer from scalability issues.
Social services like twitter do not build their backend on SQL-based databases, for scalability reasons.
Going through the Anypic tutorial and code, is a good primer. I would also recommend checking out the Twissandra project (a Java-based twitter-clone for Cassandra) just for understanding the conceptual differences when working with NoSQL vs SQL.
Good luck!