I wouldn't base a decision to accept or reject a peer-reviewed paper based solely on the abstract and introduction sections and an opinion "the problem that they have solved is a minor one." Perhaps there is more in the paper that authors haven't explored and perhaps their focus is not correct.
There's a plugin in chrome called Read Shit Faster (ugly name but what a powerful tool it is) that allows you to read the paper in a super-easy manner allowing you to detect major flaws almost instantly and know what to look for in a more thorough reading.
The order in which I read carefully these contributions goes like this:
- Abstract: What am I suppose to learn from this piece? What is it that the authors claim to have found that has not been addressed before?
- Conclusions: Yes, I go to that section right away to see if it is consistent with the abstract and if they are delivering what was promised.
- Methods: If this section has problems from the experimental plan, setup, tools, etc., I will start considering rejection.
By now, you should have seen if the language is correct or if there are major problems in this department. I collect those right away to either help the authors write a better paper or simply to justify a rejection in case there is no substantial contribution.
If at this time I consider that the authors have something worth reading, I'll read their Results and Discussion section to check for consistency with the sections that I have already read and then I will move to he references section to see how up to date is the bibliography. By the way, I would dig some extra references that are more current to suggest some improvements for the authors and perhaps to see if there's something remotely similar that has been published... Sometimes, if you know the authors, you may see if the work has been published before and point those works to the editor. Turn it in can also detect plagiarism (intentional or not) and you may point that to the conference organizers.
Typically, by the end of a Read Shit Faster session I would have made my mind in regards to reject, major editing needed, or accept (rarely) a paper. The remaining process is to document everything.