As stated in other answers, the two most likely problems are deadlocks and race conditions. However my main advice would be that if you are looking to train a team on the subject of concurrency I would strongly recommend getting some training yourself. Get a good book on the subject, don't rely on a few paragraphs from a website. A good book would depend on the language you are using: "Java Concurrency in Practice" by Brian Goetz is good for that language, but there are plenty of others.
