Is there any obvious warning when auto-pilot is disengaged or when the mode changes? Under the investigation section of the First Air Flight 6560 incident, it describes the catalyst for the accident:


  The approach was entirely flown on autopilot, which was correctly set to capture the localizer signal and track along the runway centreline (VOR/LOC capture mode). However, an inadvertent movement of the control column by the captain during the turn onto the final approach track caused the autopilot to disengage from VOR/LOC mode and revert to maintaining the current heading, resulting in the aircraft rolling out to the right (east) of the runway centreline.


My question: Is there any obvious warning (on common commercial aircraft, i.e. 737, A320) when auto-pilot is disengaged or when the mode changes?

I would have expected there to be an audible notification, some flashing light or something to make it as apparent as possible that something has changed, if it's as easy to change as 'nudging the stick'.
The Boeing 737 allows a mode called control wheel steering (CWS). The A320 doesn't. For what is CWS, see: Is it possible to disengage only one axis of a two-axis autopilot?

The wording on Wikipedia doesn't emphasize this point; however, the final report does.


  The pilots may also manually control the aircraft in a normal manner with the control wheel and column (control wheel steering [CWS]) without disengaging the pitch or roll axes of the autopilot system. Pilots can then assist the autopilot system in flying to a selected heading or course. Use of CWS does not disengage either channel of the autopilot system. The autopilot system was modified from the original design to allow for the use of GPS guidance for the course signals to the autopilot (section 1.6.10).


Note that Wikipedia says "(...) disengage from VOR/LOC mode (...)".


Therefore, for First Air Flight 6560, the autopilot was not disengaged.
Switching to CWS is not aurally annunciated. See also: Why are callouts of changes in the Flight Mode Annunciator not automated?
Autopilot disengagement is accompanied with aural and visual warnings. See: Why is an auditory alarm necessary when the autopilot disengages?




(All bold emphasis mine.)