Read the changelog. Latest update now calculates the Height & Weight perfectly, so it's more strict on edited values.
Anything modified in the PKM Editor pane could have had its Height & Weight altered.
Fixed on latest commit (after the 2/14 release..)
You can have one illegal move in a "mastered" state by selecting it in the Alpha mastered option, regardless of if the mon in question is actually an Alpha. This surprisingly works on moves not available from the move shop or even in the natural learnset of the mon as well, so I definitely think there's something aside from the base level-up mastery and move shop flags that can trigger the "mastered" state. Needs more research.
It is possible that you merely hacked the Z crystal onto the mon, but used the wrong version.
They are actually two item IDs for the Z crystal: one meant to be in the bag, one meant to be held.
I presume you made the mon hold one in the bag, hence Z-move option didn't appear in battle.