In light of the 200x series, I have come to the conclusion that the Filmation version of He-Man was already seasoned by the time we, as viewers, were introduced to him. For instance, in the Filmation series, He-Man's legend had already spread across Eternia, even to places he had never been. This leads to the conclusion that He-Man had been around awhile and probably had already matured mentally and emotionally. There was little inner conflict within Adam in the original series. He was responsible and everything he did that was irresponsible was simply a ruse (as you stated in your post).
As a character, He-Man can't develop in any other way. Adam can't continuously be irresponsible or otherwise He-Man would never save the day. The exact same thing can be said about Superman or any other superhero with two identities.
If you want to flesh out Adam's irresponsibility it's going to have to be right after Adam learns of his destiny and is struggling with his wants and desires in contrast to the needs of Eternia. This scenerio can lead to many mistakes and even tragedy (depending on how serious you want the situation to get).
You must realize that Adam can't remain irresponsible or he simply becomes another villain - sins of omission are sins nonetheless.