A B767-300 flight crew suffered autoflight anomalies on descent to OAK. An airspeed deviation and failure to meet a crossing restriction resulted.

Narrative

[We were] cleared the MADWIN FOUR arrival to OAK. Cruise descent from FL280 to cross SHARR at 12;000 feet as per arrival; aircraft in VNAV/LNAV and center autopilot. Aircraft initially intercepted VNAV path to cross SHARR at 12;000 feet; which was entered in the FMC and the MCP. Shortly thereafter we were advised by NCT that it appeared we would not make the crossing restriction. I initiated a more rapid descent using speed intervene and speed brakes extended to make the altitude restriction. The aircraft increased nose down pitch and increased speed and rate of descent; it failed to capture the speed and exceeded VMO; I reduced speed commanded via the bug to slow aircraft which was very slow to respond. ATC re-cleared us to 10;000 feet prior to reaching SHARR and requested we decrease our rate of descent. When later cleared to descend to 8;000 feet with VNAV selected the airspeed bug drove back to 240 knots; but the aircraft commenced descent without slowing. Disconnected auto flight systems and manually slowed aircraft and then continued descent; once stabilized I re-engaged center auto pilot and VNAV. Item entered in aircraft log.