So, mix-and-match existing papers? As a referee, I often do check whether the authors have published similar content before. The only way to beat this simple vetting is if someone pushes the same paper to multiple venues, and they all get accepted at around the same time. This is pretty unlikely.
Incentives for reviewing are broken. Currently researchers have to see it as an intrinsically motivated activity for the good of the field, there are no quality checks per se.
More and more journals are using plagiarism detection software to test for that. My wife recently got caught 'plagiarizing' herself after she copied a paragraph of background material from a previous paper. The journal refused to send her paper out for review until she rewrote the offending section.
Unfortunately, some publications use a double-blind review process, where checking whether the authors have published similar content before becomes more difficult: you'd have to figure out who the authors are first, which kind of goes against the idea of a double-blind review process.
But of course, when the double-blind review process is not used, then it makes perfect sense for a reviewer to check the authors' other published work. In journals that require a certain percentage of original work, I don't see any other way.
If all papers were indexed by a full-text search engine, you could simply pick a few sentences that sound unique and search for them across all publications. It's not like self-plagiarism is more important to detect than regular plagiarism :)
Or journals could just submit all papers to the plagiarism-detectors used for undergraduate work, like Turnitin.
Incentives for reviewing are broken. Currently researchers have to see it as an intrinsically motivated activity for the good of the field, there are no quality checks per se.