(1) Background: Passenger vehicles equipped with advanced driver-assistance system (ADAS) functionalities are becoming more prevalent within vehicle fleets. However, the full effects of offering such systems, which may allow for drivers to become less than 100% engaged with the task of driving, may have detrimental impacts on other road-users, particularly vulnerable road-users, for a variety of reasons. (2) Crash data were analysed in two countries (Great Britain and Australia) to examine some challenging traffic scenarios that are prevalent in both countries and represent scenarios in which future connected and autonomous vehicles may be challenged in terms of safe manoeuvring. (3) Road intersections are currently very common locations for vulnerable road-user accidents; traffic flows and road-user behaviours at intersections can be unpredictable, with many vehicles behaving inconsistently (e.g., red-light running and failure to stop or give way), and many vulnerable road-users taking unforeseen risks. (4) Conclusions: The challenges of unpredictable vulnerable road-user behaviour at intersections (including road-users violating traffic or safe-crossing signals, or taking other risks) combined with the lack of knowledge of CAV responses to intersection rules, could be problematic. This could be further compounded by changes to nonverbal communication that currently exist between road-users, which could become more challenging once CAVs become more widespread.