Con Learning curve
A lot of effort went into making OrientDB easy and familiar to use (such as SQL queries for example). However, it's important to understand the database engine a bit and how it works in general (links for example). This involves a bit of a learning curve if you're not familiar with graph databases. Not an enormous curve or anything, but it's still a consideration.
Con Not well known
It's a very unfortunate thing, but it's true. Not many people know of this gem so that makes it difficult to find community support at times. It also makes it hard to get people on board with it who shop products by brand name or flashy marketing. It also means there are less code snippets, libraries, and frameworks that consider it. While it's interoperability is good with SQL support and Tinkerpop, it still doesn't change the fact that many things don't give it much thought and that can lead to more work as a developer sometimes.