What could possibly go wrong?
False flagging, FUD based on groupthink and cognitive biases, accidental suppression of newly created websites in favor of older ones. Just to start off a list.
Not everything is solvable through algorithms. Especially if your initial goad is ill-defined. There are about half a dozen completely separate things that are being labeled as "fake news" today, from websites impersonating news agencies and pushing lies, to actual news agencies pushing lies, to viral hoaxes on social media.
Ultimately, whether a news article is fake or not is determined by its relation to reality. You could use context as heuristic to filter out complete garbage, but this is something that's actually being abused by many subcategories of "fake news" to begin with.
People should be able to use their own judgement to spot nonsense, without algorithms telling them what to think. If they can't, the first questions should be "why?" and "why now?", not "how do I make an app to fix it?".
Personally, I think the underlying assumption behind current social media are profoundly broken and can't be fixed just by sprinkling more tech on top of it all. Obvious example: if you release a news-checking app and someone else releases a fake news-checking app, how do you expect your users to choose the right one?