I believe that I found an exploit bug in training. I was at level 26 and 5 ticks away from leveling up. In Riften, I engaged in Smithing training. Without leaving the dialog screen, I purchased all 5 levels of training. This caused me to level up. I exited the dialog than reentered it to find I still had all the gold I paid for training, the dialog claimed I'd trained 0/5 times at this level, and had the save Smithing skill level as before I trained, including the same partial level progress. I left the dialog and checked to confirm that I had indees leveled upto 27. Not wanting to cheat, I reloaded a previous save.

Has anyone elae seen this problem? Achieve a new level while training causes the trainimg to never have happened, though you keep the level.

Not an exploit, its a "feature".

Kidding aside I honestly think its intentional. You are allowed 5 skill training sessions per level maximum, as the training screen says. This resets when you actually level (as in: choose +10 health/mana/stamina, you can save perks), not when you see the level bar fill. This can be convenient when you have septims in excess, and know there's at least one skill you hate grinding and would like to train. When you hit the level, save the +10 stat boost until you get back to town, find a trainer and use the 5 skillups. Honestly I'm consistently too lazy to bother with training, but its convenient if you like to min/max.