B767-300 pilot reported malfunction with FMC and MCP inflight.

Narrative

After takeoff; VNAV was selected and shortly after the airplane turned right complying with the departure procedure. In the turn; the airplane exceeded 30° of bank; stopping at approximately 33/35° of bank. The 'BANK ANGLE' aural warning sounded. The First Officer disconnected the autopilot and returned to a standard rate turn. Subsequent to the turn; with the airplane flying straight and level; we reengaged the auto pilot. Shortly after; the airplane turned left once again approaching 30° of bank. It stopped at 30° of bank but did not sound the warning this time. The airplane returned to straight and level flight flying the departure procedure. Later in flight; on the arrival into ZZZ; ATC gave us a speed instruction. We entered that into the FMC. That appeared to freeze the FMC. The airplane stopped descending briefly then was slow to descend after that. It showed on path; but we weren't convinced of that. In light of a recent conversation with a 767 airplane specialist on a similar issue with this aircraft; I felt the Mode Control Panel (MCP) needed to be reset. The airplane was flown manually while I turned off both flight directors. I waited a couple of seconds; then reengaged both flight directors. That appeared to wake up the system. The autopilot was reengaged. The airplane then started a normal descent one would expect at this part of the arrival and flew normally after that.Continued apparent malfunctions of the Flight Management System. An entry was made into the aircraft logbook. Maintenance apparently did a reset last time I wrote a similar issue up. In speaking with a 767 specialist; he felt the MCP should be replaced. In light of the continued issues we have had with the airplane; that sounds like a great idea. The mechanic onboard for the past few legs verified the airplane was behaving normally up until the events described in this report. However; the previous mechanic confirmed anomalies with the airplane not capturing the altitude correct correctly on previous flights he was on. I believe an extensive troubleshooting of the Flight Management System and Mode Control Panel is in order.