Journal standards vs. personal standards I am currently reviewing an applied math paper that I don't think is great; indeed, I am hesitant to accept it even with major revisions.  The language is poor, I'm not convinced by the arguments, and the numerical results are difficult to interpret based on how they are presented.  However, based on other work this journal has published (in particular, other papers by the same authors), I think the quality of the journal I'm reviewing for is a bit lower than my personal standards.

Should I based my final recommendation on my own standards, or the journal's?
There are many different notions of quality of a paper:


accessibility of the presentation,
soundness of the arguments and conclusions,
relevance of the research.


Ideally, the level of journals only differs in Point 3. Realistically, there are some differences in Point 1 as well (ironically, I find that middle-level journal score best here, but that’s a different story). However, even mega journals aspire Point 2 – and outrage ensues if they clearly fail.

I would therefore not let the level of the journal influence assessment of deficiencies with respect to soundness, i.e., if I consider a paper unsound, I recommend to reject it, no matter the level of the journal.
Also, think for a second what would happen if all reviewers would recommend to accept all papers that are better than the worst paper in the journal in question:
Due to the variability and laziness of reviewers (and the abundance of bad papers), the threshold would decrease perpetually.
Nobody wants this.

Also, irrespective of the journal’s level, I note everything I see wrong with a paper, and let the editor decide whether this is a sufficient reason for rejection. As language problems (and some other presentation issues) can be fixed by a copy editor or similar, I would not even let them influence my main recommendation, but just recommend heavy copy-editing or similar to the editor.