So, false positives may not matter in some conditions. Ireland is currently reporting anything from 5 to 30 cases per day, doing anything from 3000 to 10000 tests per day, and has capacity for at least 15000 tests per day. If the app doubles the number of tests being done and finds a few new cases, that's fine; it's still a lot better than NOT finding those cases.

These apps would, granted, be far less useful in places with major ongoing outbreaks and inadequate testing infrastructure; lockdowns should be used to bring numbers down to the level where this sort of thing is workable.

(1) is probably a greater problem. Ireland has about 30% uptake, which probably isn't enough.