How insecure are app stores?

It has not been a good week for lovers of apps, which is pretty much anyone with a smartphone. Both Android and iOS apps have been infected with malware, apps that were available through the official app stores rather than illicit third parties. Millions of users are at risk from the resulting malware infections, despite the Google 'Play Store' Bouncer and Apple's iOS 'Walled Garden' which were meant to prevent such breaches. So what went wrong, and how can it be prevented from happening again?