Buttercup's Berserk Button of being called "Princess" makes a lot of sense, since she's a Tomboy, but also because one of her enemies is named Princess, so when someone calls her that, it sounds like she's being compared to the Spoiled Brat who wants to be a Powerpuff Girl. Of course she'd be furious!
A video released on Cartoon Network's YouTube channel reveals the series to be a continuation of the original, not a reboot. Suddenly, the other Darrins for the girls make sense: they're SUPPOSED to sound older to reinforce that time has passed since the original series. It also explains why the Professor sounds aged, as well, why the girls are in elementary school, and the sudden appearance of modern technology such as smartphones.
The use of the "No Me Gusta" meme actually makes more sense when you realize that Bubbles speaks Spanish, meaning that this is probably just as much a Call-Back as it is a meme.
If you think about it, Bliss's traits that make her seem like a Mary Sue sort of make sense in the context of the show, as the Professor was trying to create the "perfect" little girl. It's possible that some of her Sue-like traits (such as her overly long and complex full name) might have been deliberately invoked.
Bubbles being a coder/good at computer programming is this if you think about it. What's her special ability again? To perfectly understand multiple languages! And since programming is sometimes referred to as a language itself, it makes perfect sense for Bubbles to be able to understand it.
You know, Sapna never specified if it was just romantic love that made her turn into a giant spider...
In "Painbow", why didn't the rainbow have any effect on the Powerpuff Girls? They looked directly at it.
Well, the girls aren't really like any normal human, being created in a lab and all, so maybe they don't get immediately affected by Allegro's powers (until the Party Lobsters directly put Bubbles and Blossom under control). Alternatively, one of the ingredients used to make the girls was "everything nice", which may make the Powerpuff Girls immune to the rainbow's powers since they already have "niceness" in their bodies, "something nice" can't really affect them just by looking at it.