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?
EDIT (clarification): even though it seems to be a specialized case, it's really about etiquette regarding criticism of other authors' papers.