I watched the falling leaf.

• In this case, "falling" is acting as an adjective.
• You CAN cancel "falling" because it is not an essential part of the sentence.
• The base clause of this sentence is "I watched the leaf".
• This base clause is transitive (SVO).

The movie was confusing.

• In this case, "confusing" is also acting as an adjective.
• However, in this case, you CANNOT cancel "confusing" because it is an essential part of the base clause. (It is the complement of "movie").
• This sentence cannot be simplified further.
• The base clause is equative (S=C).

The leaf is falling.

• In this case, "falling" is the 2^nd part of a two-part verb, "is falling." (The helping word "is" and the -ing form of "fall" are working together to form the continuous tense of the verb "to fall").
• You cannot cancel "falling", because "is falling" is the main verb of the sentence.
• This sentence cannot be simplified further.
• The base clause is intransitive (SV).