I had the same problem, and it turns that the problem is actually in the error message - its confusing. If you look at the exact protocol bytes read by the server (which you removed - here is the relevant part from my log):
ssl_engine_io.c(1854): | 0000: 15 03 01 00 02
ssl_engine_io.c(1854): | 0000: 02 28
The 0x15 refers to ContentType 21, which is an alert message. "03 01" is the version and "00 02" is the length of the actually message.
"02 28" means fatal error 40, and refers to a handshake_failure, which simply means that the server didn't offer anything that the client could use. In other words, the Nokia don't have the required root certs to recognize your ssl cert.
When this error occurs, the server protocol state machine is waiting to read the optional client certificate. So the "SSLv3 read client certificate A" is simply the server reporting what state it was in when it received the alert message from the client.
Just slightly confusing.
Best Answer
No, it will not break HTTPS connectivity to your website; TLSv1 (and newer versions, if your software is recent enough) is already being used instead by almost all browsers (with the notable exception of IE6 on Windows XP).
Verify in your configuration that TLSv1 is enabled, but it is by default in almost every server-side SSL configuration.