Not only are there privacy implications in terms of what the vehicles will be transmitting locally, vehicles also need to have a network connection as well to receive new certificates and certificate revocations:

    Under the proposal, each message will be digitally signed. Each car
    will be provisioned with 20 certificates (and corresponding secret keys)
    per week, and will cycle through these certificates during the week,
    using each one for five minutes at a time. Certificates will be revocable;
    revocation is meant to guard against incorrect (malicious or erroneous)
    information in the broadcast messages, though there is no concrete proposal
    for how to detect such incorrect information.

This regulation will force all cars to be connected cars, and being connected comes with its own security and privacy implications.