DaveReidUK thanks a lot!
There is a significant number of planes flying with bad aircraft addresses
There are indeed, although a "bad address" won't necessarily duplicate one belonging to another aircraft (there are 16 million possible combinations).
The EASA document explains it this way:
"Any incorrect aircraft address is, potentially, a duplicate address, because it has not been legitimately assigned to that airframe. The potential for duplication rises dramatically in cases of incorrect addresses where values such as all 0’s or all 1’s have been set."
Regarding TCAS it says:
"The performance of ACAS II systems could be seriously degraded or even disabled."
But there are certainly documented cases of aircraft airborne simultaneously in the same airspace (including the London TMA) and sending the same address. While that would affect the Mode S information that the controller sees, both aircraft would still be responding independently to Mode A and C, so radars that use code-to-callsign conversion should still be able to identify both.
You can still differentiate between the planes using the assigned squawk code?
Can all equipment do code-to-callsign conversion?
Would the controller need to recognize there is a problem and switch modes?