Somebody (e.g. Billybob) does something stupid that winds up on the local news sites. 6yr later the court case is long since closed and he wants it behind him because it was a just a drunken mistake. EU says he has a right to be forgotten which he exercises. Google deference the news articles from Billybob's name. Billybob Google's himself and finds a blog about Google referencing search results that mentions him by name and the nature of the result. Since it mentions him by name it's a primary result (you Goggle Billybob and it comes up) and Google should have to remove it per the law.
Obviously this sort of law creates an incentive for background check services to just crawl every news site imaginable which could create a whole set of different problems but that's beyond this scope...
I think it'll just take time for society to understand that people do stupid shit and ignore it as long as it's irrelevant to the context and "forgetting" events is just a stopgap. Eventually people will realize that racists, political extremists and people with non-violent felonies can still function normally from 9 to 5 and this will be a non issue.
This problem has a lot in common on the technical side with dragnet surveillance and law enforcement. Google needs to determine what is and isn't relevant when returning results for somebody. Some misdemeanor in highschool is of dubious relevance 10yr after the fact and if the person apparently has a lot of results that paint a picture of them having a successful career and generally having moved on. Google could put that on the 3rd or 4th page, after all the "people named $name in $state" public records databases, where it's practically forgotten. Meanwhile the NSA (or whoever) needs to figure out how to filter out and avoid flagging for followup that sound like flags but are actually sarcastic, based on inside jokes, or obvious false positives when considered in context (to avoid wasting their time,wasting our money and violating people's privacy).