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.
Crowning Moment of Heartwarming: Many, but the earliest comes at the end of the first episode, when the cat owner's boyfriend - who had never considered himself a "cat person" and would have rather had (in his own words) a tiny, annoying dog than his girlfriend's two cats - offhandedly refers to the kitties as "my cats." When he realizes what he's just said and how far his relationship with the cats has progressed, he has to reiterate it to Jackson with obvious delight and pride.
Squick: Whenever an owner has an inadequate litterbox, Jackson takes out a blacklight and usually reveals urine stains everywhere except the litterbox.
Or if the litterbox itself is fine, but the owner has been negligent in cleaning it out.
Also, how does Jackson sometimes inspect the litterbox? By running his hand through the litter. True, it's to gain information, and he acknowledges that it's gross, but still.
50% of season 5 was filled with the above examples.
Tear Jerker: Occasionally, Jackson meets an owner who had recently lost a pet and finds it hard to move on. Often, when this happens, they memorialize the old pet as a way of symbolically letting go. One of these episodes even had an "In memory" card for one of Jackson's own pets at the end.