Just imagine how easy it's going to be to screw over other websites, just by making an account, uploading material that could in some way be construed as violating copyright but passes the filter because it cannot be perfect, and then reporting the site to one of the bodies responsible for upholding this directive.
Hell, just by doing that you could probably end any potential upholding of this system really fast.
Maybe someone (with a big following on Twitter, let's say) needs to start compiling a list of national government and EU websites that publish user generated content, for example petition sites. If the law goes through, people can go to those sites and post "unexpectedly copyright infringing" content, such as a paragraph from a book (perhaps a self-published one that consists of just seemingly contextless paragraphs).
(Inb4 the national laws end up including huge exemptions for site run by the government or political parties).
A more technical campaign would be reverse engineering the filtering algorithms (censorship machines) that sites end up forced to install, and finding a way of generating new copyrighted content that has the equivalent of a "hash collision" against already popular (or political) content hosted on websites using the filter.
Chans allow anonymous users to upload images and historically this leads into a lot of illegal content, especially stuff like child porn, to be uploaded unless you have strict moderation.
That's 4chan. The other big site is 8chan, where users can create their own boards and there are less rules, which makes it much harder to moderate. Then you also have all of the smaller chans which tend to get spammed by bots posting illegal stuff like child porn.
That will be funny