The entire game is an unnatural a sequel as it gets. The entirety of it is a retcon. To start off, it invalidates two aspects the ending of the original game. One of them being that Chell escapes the lab, and the other that GLaDOS was exploded to shit.
And then it invalidates several more core themes of the original. Aperture Science is no longer an actual science facility. The "research" they conduct and their attitude towards science is so god damn goofy that it makes it extremely implausible they'd come across any actual inventions like the Portal Gun. Remember that reference to Black Mesa, the one that basically said Aperture Science is a relatively small and effective facility in comparison? Nah, they're actually fucking humongous and their course of progress is "throwing stuff at the wall and seeing what sticks".
Then the stupid writing.
-An AI that took up what amounted to cubic meters upon cubic meters of hardware functions perfectly fine inside a potato.
-An AI:
A) Is supposedly created from a human, yet never functioned remotely as one. That's a huge logic gap standing on top of a retcon. This plot point is only introduced in the second game and runs contrary to the first game's canon, namely that being a purely science-oriented AI, GLaDOS needed personality cores to constrain her. What the fuck is the point of her being a human before?
B) Then realises its origins by hearing her old boss speak. Because that's how computers work. They don't have access to their own memory banks.
-Right at the moment Chell is in GLaDOS's hands, the AI decides to let her go. Because she's "tired".
And to top it all off, the story goes nowhere. Absolutely bloody nowhere. It introduces a couple of completely unnecessary, contradictory and/or stupid concepts, like the things I mentioned, and then proceeds to end right where the first Portal ended. For no good reason, either.
This is off my memory because I played the game a year ago, but yeah. And I ain't even touching Wheatley.
It's a goofy, child-oriented little game that only achieves cuteness. To call it a storytelling masterpiece on almost any level is, in my opinion, insulting.
