In Part I of the Legion Rejects, I noted the four basic reasons that the Legion rejected applicants:
1. Fake powers.
2. Undependable powers.
3. Useless powers.
4. Limitation on powers.
Bizarro Superboy was rejected in Adventure #329 for reason #2. Of course, it wasn't so much that his powers were undependable as that he himself was undependable.
The next group Legion tryout after Adventure #325 came in #330.
Ethel was an eyeful, alright! And the Mess seems obviously a rip-off of the old Charlie Brown character, Pig-pen. Both were clearly rejected for reason #3. Update: Norman points out in the comments that the Mess probably took his rejection with a "What, me worry?" attitude. ;)
In Adventure #331, Dynamo Boy (a villain) has successfully gotten rid of all the members of the Legion, and conducts his own tryouts. He adds a reason #5 for rejection:
Obviously, this is not normally a disqualifier for the Legion. I'm not sure if Animal Lad (whose powers were changing humans into animals, and taming animals) ever came back for a tryout after Dynamo Boy was captured and expelled.
However, Dynamo Boy does use the normal criteria for some of the other applicants:
Golden Boy is a reason #3 reject, as is the Polecat:
Rejected for reason #2 after he found himself unable to withdraw his tusks from the tree.
The next Legion tryouts came in Adventure #337. Four Legion members had gotten married (Lightning Lad/Saturn Girl and Ultra Boy/Phantom Girl), and replacements were needed. This was all a plot to get three evil aliens to join the Legion, and so the rejects were just Night Girl and Chlorophyll Kid again being rejected for reason #4 and #3 respectively:
In Adventure #342, Calamity King got gonged for reason #2:
While Color Kid was a #3 reject:
He later proved that his power had some value. In Adventure #351, a green Krytponite cloud surrounded earth during the Legion era and Superboy and Supergirl were forced to resign temporarily. However, he came up with a solution in #352 by turning the cloud to blue Kryptonite, which only affects Bizarro.
Adventure #346 introduced a new wrinkle.
Qualifying tests presumably meant that there would be fewer rejects, and indeed the four applicants show above (Princess Projectra, Ferro Lad, Karate Kid and Nemesis Kid) were all accepted into the Legion, although Nemesis Kid could arguably have been rejected for reason #4:
Indeed, I remember one occasion where he was captured by Duo Damsel, precisely because while he could defeat any one opponent, he was a wimp when facing multiple foes.
That takes us through Adventure #350, another good breaking point.