“Failures” here does not necessarily mean that Jo thinks Jack and Ned have become thoroughly bad men. It is better understood in terms of Jo’s goals as an educator. She judges the Plumfield boys partly by whether the moral education she tried to give them produced the kind of adulthood she hoped for.
That helps explain the apparent contradiction concerning Ned. In Little Men, Ned is introduced as a bully and belongs to the rougher group of boys. By Jo’s Boys, however, Alcott can call him “good-hearted” and show him making the long journey from Chicago because he genuinely cares about his old friend. Those facts indicate that Ned is not simply an adult villain who learned nothing at Plumfield.
Rather, Jo's category of “failures” is broader and more personal. Some of her former pupils have developed into the unusually admirable, purposeful men and women that Plumfield was intended to produce; others have fallen short of that ideal. Jack and Ned apparently belong to the latter group. Jo can therefore consider Ned one of her educational disappointments while still recognizing that he possesses affection, loyalty, and a fundamentally good heart.
Jack's case is easier to understand because his dominant childhood fault is selfishness. In Little Men, his greed and dishonesty cause considerable trouble. Nothing we hear later establishes the kind of conspicuous moral transformation that would make Jo regard her attempt to reform him as a success. The absence of further bad behavior does not necessarily mean that Alcott intends us to infer a complete reformation.
There is also an important nuance in the wording:
“what Mrs. Jo called her failures.”
Alcott does not simply announce that Jack and Ned are failures. She attributes that judgment specifically to Jo. That leaves room for Jo's characteristic tendency to take personal responsibility for the children she has educated. “My failures” can mean something closer to “the boys with whom my educational experiment did not accomplish what I hoped” than “these men are worthless.”
Ned's later appearance actually reinforces this distinction. His affectionate response demonstrates that human beings cannot be neatly divided into Plumfield “successes” and “failures.” Whatever shortcomings remained, Plumfield evidently did leave him capable of deep attachment and loyalty.
So there is no real need to assume that Ned remained the same bully he was as a boy. Nor must Jack still be committing the same offenses. The phrase refers primarily to Jo's assessment of the results of her moral and educational work, not to a declaration that the two have no redeeming qualities.
In fact, calling Ned “good-hearted” later makes the point particularly well: a person can disappoint an educator's highest hopes without being a bad person.
