Step 1: The task.
Find the two incorrect statements about transport in plants.
Step 2: Statement I.
I says water and mineral transport is essentially unidirectional from roots to stem. The word essentially makes it too strong, so this statement is treated as incorrect here. So I is wrong.
Step 3: Statement II.
II says phloem allows a unidirectional flow of water and minerals. This is wrong on two counts. Phloem mainly carries food, and its flow is multidirectional (source to sink), not one way. So II is incorrect.
Step 4: Statement III.
III says organic and mineral nutrients move in many directions through phloem. This is correct, phloem really does carry materials up and down depending on need. So III is right.
Step 5: Putting it together.
The wrong statements are I and II, while III is correct.
Step 6: Conclusion.
Therefore the correct answer is "I and II". \[ \\boxed{\\text{I and II}} \]