Q:

Why did Jo consider Ned and Jack to be failures?

In Jo's Boys in chapter 5, it is stated, 

Jack and Ned sent regrets and best wishes, and no one mourned their absence; for they were among what Mrs. Jo called her failures.

Why were these two in particular considered to be failures? From the second chapter of Little Men (as well as other incidents in the book), we know that Jack is a greedy dastard, so I'd expect that vice to be what Jo is disapproving of. In Ned's case, chapter 2 of Little Men says he is a bully. But are we expected to believe that he continues to be a bully?
In chapter 15 of Jo's Boys, it is stated, 

...while good-hearted Ned traveled all the way from Chicago to press their hands and say, with a tear in his eye: ‘I was so anxious to hear all about the dear old boy, I couldn’t keep away.’ 

The text describes Ned as kind-hearted, so one might expect that he has improved somewhat. For that matter, the other times Jack is mentioned in Jo's Boys don't seem to paint him negatively. So why does Jo consider them failures? 

A:

Right from the beginning of Little Men, Jack and Ned are portrayed as inherently flawed:

Jack Ford was a sharp, rather a sly lad, who was sent to this school, because it was cheap. Many men would have thought him a smart boy, but Mr. Bhaer did not like his way of illustrating that Yankee word, and thought his unboyish keenness and money-loving as much of an affliction as Dolly's stutter, or Dick's hump.
Ned Barker ... bragged a good deal about what he could do, but seldom did any thing to prove it, was not brave, and a little given to tale-telling. He was apt to bully the small boys, and flatter the big ones, and without being at all bad, was just the sort of fellow who could very easily be led astray.

Unlike, say, Dolly's stutter (an unfortunate affliction) or Stuffy's greediness (the result of parental overindulgence), the flaws that Jack and Ned have are seen as something wrong with their character, as moral failings. Nothing in the course of Little Men changes that assessment or causes us to feel sympathy for them. For example, Jack steals Tommy's money, and is perfectly happy to let Nat bear the burden of suspicion; when Ned grudgingly begins to accept that Nat might not be the thief after all, he bullies Nat to try and get at the truth. 
Alcott does show that each boy has his virtues as well. Jack does eventually confess to the theft and try to atone; Ned does treat Nan with disinterested affection. But for all that, neither Jack nor Ned form any significant connections with their fellow students at Plumfield. Every other boy or girl has at least one close attachment: Dan with Nat, Demi with Daisy, Tommy with Nan, Dick with Dolly, and so on. Through such attachments, the students become part of the larger Plumfield community and show the success of the school's methods.
Jack and Ned evidently haven't formed any such bonds with the community. Their careers after Plumfield show that their inherent nature is the same. Jack is still "money-loving"; he is a businessman "bent on getting rich". And Ned is a lawyer; nuff said. 
Joking apart, the reason they are "failures" is precisely that "no one mourned their absence". Unlike the other boys (and random girl or two) of Plumfield, Jack and Ned have not made themselves part of the place. So when Nat is on the verge of departure for the untamed wilds of Europe (let us remember what a barbarian place it was in the 19th century, especially when seen from the vantage point of the high culture and civilization then prevalent in America), the rest of the community gathers to wish him farewell; Jack and Ned are not connected enough to feel drawn to participate, and worse, nobody cares that they aren't part of the gathering. Is there a greater indication of failure in life than that your presence or absence makes no difference to anybody?

