One recurring trend I've noticed with Petrie is that in certain movies and TV episodes, the filmmakers introduce some unexpected new quirk to his character that is never again referenced in another installment. Besides his religious treatment of the Bright Circle Celebration in the titular episode, examples I've noticed include his penchant for imaginary friends in LBT IX, his snuggling stick in "Days of Rising Waters", and his superstitiousness in "The Meadow of Jumping Waters". I suppose not all of these are necessarily indicators of immaturity, though.
Also, is it just me, or does Petrie behave more "maturely" when he is forced to act on his own, as opposed to when he is with his friends, who generally seem to make decisions for him? For example, when he is trapped with Guido inside Blackrock in "The Hermit of Blackrock", he himself notes that Guido is more frightened of the situation than he is. Petrie's behavior throughout that entire episode struck me as less panicky, and more rational, than is typical of him.