These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Common Mary Sue Traits: Pichi sports a few. Namely, having blue eyes (an unusual eye color for Pikachus, who usually only have black eyes), wearing a sky blue bow, having pink cheeks instead of red, her voice being mentioned to sound like a new born babies, and managing to beat Ursaring after it nearly killed Pikachu, granted though it was through indirect means. Considering the nature of this fic though, this might have been intentional.
Fridge Logic: The fact that it never accrued to either Pikachu or Pichi to just tell their trainers about eachother instead of being forced to go their separate ways at the end. Given Ash's past track record, he would have been more than accepting of it and likely would have been willing to have a few more traveling companions if it meant Pikachu would be happy, and from what we hear of Faith from Pichi she sounds nice enough and would probably understand as well. Sure, it would of probably bought them the rest of the region together at most but at least it's better than being forced to split up after only three days of only just getting to really know each other, and likely never seeing each other again.
The Woobie: Pikachu of all Pokemon. ESPECIALLY at the end when he decides to stay with Ash. If Misty hadn't already gave him a hug and started to confort him shortly after, the audience might have instead.