This has epidemiological consequences, as acknowledged by one of the leaders of the DP-3T team to the BBC: https://www.bbc.com/news/technology-52995881
Apple (and Google?) retain higher quality signals than what they make available to the apps.
It introduces new security issues, because Apple and Google have had to make choices that degrade the qualities of the protocol. See Sections 3.5 and 3.6 in the report. The Swiss Cyber Security Centre expressed negative sentiments towards the fact that Apple and Google didn't implement some of the recommended protocol improvements: https://www.melani.admin.ch/dam/melani/de/dokumente/2020/Rep...
Finally, this Bluetooth layer becomes a covert channel for transmitting information between phones. There is a lot that we can't tell from this outside.