I keep wondering if package managers (be it Google Play, apt or dnf) are in need of a solution like Certificate Transparency. Like Certificate Transparency, it would not necessarily prevent a backdoor(/certificate) from being pushed to selected users, but it would guarantee detectability, at least after the fact. If the package as a whole is included in the log, it would also allow BinDiff-style reverse engineering of any backdoor. Application developers could scan the log for unauthorized builds of their software (i.e. key compromises), and I imagine there are some things you can do with gossip protocols for end-users as well (i.e.: how popular is this build? Am I the only one running it?).
This would solve part of the trust issue both for proprietary and open source software (I mean, who's actually using or verifying reproducible builds?). It would also be a huge problem for intelligence agencies or other adversaries who want to do this undetected.