It seems that only the first statistic used for each criteria base (stat.useItem, stat.mineBlock, etc.) within "/scoreboard objectives add <name> <statistic> <display name>" actually behaves correctly. For example, I created an objective for stat.useItem.383 (Spawn egg) and it worked fine but if I try to make an objective for another item like: stat.useItem.<item> it does not increment with each use. The same happens with stat.mineBlock, I created an objective with stat.mineBlock.1 (Stone) and it worked fine but it did not work when I created one with stat.mineBlock.2 (Grass Block).
Edit: I think the problem is only existent within "stat.useItem" but Grass Blocks do not work with stat.mineBlock.2 for some other unknown reason.