He's talking about a couple of recent very clever timing attacks on JSSE. However they are not comparable to Heartbleed or this SChannel overflow in severity at all:
(1) They require you to have a pre-recorded SSL session you're trying to crack. Random script kiddies won't find it useful.
(2) They require sending a lot of traffic to the server to try and break that single recording (you can get caught quite easily!)
(3) They don't reveal the private key, only per connection premaster secrets (if I understood correctly).
Basically, the first attack was possible because JSSE returned "internal server error" when faced with a particular kind of malformed packet instead of "bad padding" - this binary yes/no thing was enough to allow the attacker to divine some internal state and with enough queries retrieve the PMS. The second was a similar trick but instead of observing a different error code, it exploited the fact that internally the code was throwing an exception and this made a difference of some microseconds in the response. Over a LAN, with enough queries, that was enough to eventually reveal the PMS. However when running over a much noisier environment like the internet, number of queries required goes up quite a bit. I believe, they did not test that.
As I said before, they were both fixed, and I think Rich now agrees with me that they were fixed. There may be others that would require compiler support or hand coding of assembly to fix. Certainly there's nothing in the design of Java or the JVM that makes that impossible however. Stuff handling key material is only a small part of the overall SSL picture.