Including a segment of constructive criticism of another paper in my manuscript I'm currently investigating a subject that has theoretical and algorithmic aspects. I have my theoretical background that I think is novel enough.
As for the algorithmic aspect, I found paper X (not written by me or anyone I know personally) to be genuinely very good, but I think that using my theoretical advances I can improve it further, especially for my own application which slightly differs from the one the authors of X had in mind.

Now, after I analyzed and scrutinized X's algorithm in practice (i.e. obtained the source code and performed numerous experiments), I found that some of their assumptions and declarations are inaccurate. [E.g., if their algorithm consists of stages A->B->C->end, and they claim A makes a big difference and is their novelty, I find that it is in fact a good implementation of C that makes that difference.]

I certainly don't mean to undermine or criticize them because it is a good paper. However, I do find some discrepancies. So, in my paper, should I also include some subsection in which I specify these issues (with suitable justifications), or will it just look as nitpicking or otherwise negative behaviour on my part?

Thanks.

EDIT (clarification): even though it seems to be a specialized case, it's really about etiquette regarding criticism of other authors' papers.
If you make choices that only make sense if the article contains mistakes, then point out those mistakes to justify your choices. Then it becomes a matter of necessity to point out the mistakes, not one of nitpicking.
However as a matter of courtesy and due diligence, you could contact the original authors to ask them about the mistakes. Be sure to approach the subject gently. Along the lines of: "in the article you state that A was the cause of the performance gain, but in my tests I found the performance gain in C. As you see in these results.  Do you know what I did differently than you?"