In the original Zelda 1, Link cannot push blocks from the left or right side unless he is aligned fully on the same horizontal row of tiles with them.
In ZC, he can be standing half a tile above the position of the block and still push it from the left or right.
Example:
1st quest level 1, room right before "EASTMOST PENNINSULA IS THE SECRET". Line up Link with the block and the side doors, then walk half a tile up, then try to push the block. In ZC you can, in Z1 you can't.
This is more of an inconsistency with the original Zelda 1 than a programming bug. But it's also been in ZC for as long as I can remember. So I would really suggest fixing it with a quest rule, since hard-coded-fixing it has the potential to break any existing quests using block-pushing puzzles with limited walking space. (If there are any, anyway...I personally haven't seen such an example...)