Relative to other NoSQL databases, Neo4j does not have a lot of anti-patterns. However, there are some common troubles that seem to befall new users, and we will try to detail them here.
Using relational modeling techniques can lead to trouble with almost every NoSQL database, and Neo4j is no exception to that rule. Similar to other NoSQL databases, building efficient models in Neo4j involves appropriately modeling the required queries. Relational modeling requires you to focus on how your data is stored, and not as much on how it is queried or returned.
Whereas modeling for Neo4j requires you to focus on what your nodes are, and how they are related to each other. Additionally, the relationships should be dependent on the types of questions (queries) that your model will be answering. Failure to apply the proper amount of focus on your data model can lead to performance and operational troubles later.