Almost every single character in the play is looking out for numero uno. Most of them won't hesitate to double-cross a friend—and then double-cross their new friend to boot—when it serves their interests. In fact, pretty much the only reason why England doesn't get conquered at the end of the play is that the rebel English lords (Salisbury, Pembroke, and Lord Bigot), who have already betrayed King John, learn that Louis plans to betray them, so they betray him and become loyal to John again.
Not exactly an inspiring message, is it?
The only unquestionably good character in the play, Arthur, nearly suffers an excruciating death, only to suffer a somewhat less excruciating death through a stupid accident. That's often the fate of good characters when the Shakespeare play they're in isn't a comedy.
This play sounds like a pretty big downer, right? Well, it doesn't have to be: just check out the two big speeches by the Bastard (1.1.186-227, 2.1.588-626), in which he tackles the problem of the corruptness of the world head on—and tries to put a positive spin on it. Of course, you could also say that for a person to be able to put a positive spin on this sort of thing is the most depressing thing of all…