Übrigens and im Übrigen both mean incidentally/by the way. Are there any differences at all between the two?
First I want to say there are different "feelings" attached to them, but most of the people are not very sensitive about it. So using the one or the other it will never be very wrong.
Übrigens schuldest du mir noch Geld.
Im Übrigen schuldest du mir noch Geld.
The first sentence is what you would throw in during a conversation because it just sprung to your mind: "No offense, but by the way, remember you owe me 5 Euros?"
The second has some slight undercurrent of accusation, like in "No, I can't help you out AND furthermore I want my money back" – or maybe also defense.
Im Übrigen habe ich meine Argumente genau überprüft.
This nears außerdem or darüber hinaus – generally adding to a topic. The "by the way"-statement is made with übrigens.
Ach übrigens, gestern habe ich gelesen, dass die Milch teurer wird.