I see four main types of potential issues with proximity tracing apps:

1) Opaque/centralized mass profiling

2) Insufficient epidemiological/practical efficacy

3) Everything related to how governments implement them, e.g. making them (de-facto) compulsory

4) Mission creep

The Google/Apple approach *may* largely prevent (1) by governments.

G/A probably have still access to some data. They must amend their ToS with legally binding statements that STRICTLY prohibit them from exploiting any of it. In this case, (1) is perhaps largely resolved.

The other issues are challenging enough.

There is a heated debate with regards to (2). Concerns include large numbers of false positives/negatives, misuse, a lack of follow-up testing capacity, generally an over reliance on tech while ignoring other stuff. And of course the question of adoption, which is related to (3).

But I also wouldn't rule out the possibility that proximity tracing may be a relevant part of a strategy in the next months.

So, I currently see (3) and (4) as main issues.

Those may largely depend on the degree of authoritarianism and the health of public debate in a country.

The ways of how governments could turn such an app into a system of digital social control are potentially unlimited, even if opaque mass profiling is impossible. They could make it compulsory or require it to get tested/treated or to enable free movement. https://twitter.com/WolfieChristl/status/1245695231259000833

On the other hand, it's important to consider that we already experience massive (temporary) restrictions of fundamental rights, because there is no other way to fix this dystopia.

Of course, also private institutions e.g. employers could make such an app (de-facto) compulsory.