Narrative:

So we had multiple strange events on cruise and descent. During cruise we noticed an execute light on the FMS. Neither of us was sure what the execute light was for and the captain scrolled through the FMS pages to try to figure out what wasn't executed. We were in normal cruise as I recall and had recently stepped to fl 370. Somewhere through the scrolling of pages the plane went into continuous thrust mode and started slowing down to drift down speed. Neither of us executed the drift-down. Neither of us even attempted to get drift down speed and altitude during the short flight to ZZZ. So I was not the designated flying pilot for the flight but I had control at the time and overrode the auto-throttles to keep us at cruise speed while the captain attempted to fix the FMS and get us back to econ cruise speed. Nothing happened but we were told by maintenance after the flight that the aircraft had done something similar on a previous flight. Secondly; on the descent while on the VNAV path the captain extended the speed brakes and we got an 'unscheduled stab trim caution and an autopilot caution.' no one touched the electric or alternate trim and the autopilot stayed engaged. We did not notice any changes in the aircraft. When I was about to run the QRH the message went away and we continued and mentioned the situation to maintenance. And on the ATC side; not to be whining; but we did get the tight visual approach inside the final approach fix. The captain went off automation as the glideslope would not have been able to be tracked on the ap. We started out high and then ended up low on the glideslope with a correction. We were able to make the 1000 foot stable gate on the glideslope just barely. However I am noting these things because it is my opinion that ATC needs to stop treating heavy boeing 767s carrying cargo like we are crjs capable of making aggressive last second maneuvers in the landing pattern. I realize that some of us more aggressive pilots can use skill to make things happen; but we should not have to. ATC needs to treat us like every other heavy; low maneuvering jet. This sort of situation could lead a less experienced pilot to make a mistake.for the drift-down situation; I felt we did a good job preventing the situation. No one freaked out or did anything radical and we corrected the problem. The unscheduled stab trim was handled without any major issues. However we are occasionally getting these strange cautions on the auto-flight system that pop up and then disappear. We shouldn't be getting them at all if the plane is not having any problems. It makes you have to decide whether you run a QRH or not and whether you need to write it up or not. It also creates a distraction and a feeling of distrust on the aircraft. This is not a good feeling; especially considering recent events. As to the visual approach; the captain probably could have said 'no' to the tight vector to final. We were in a left downwind to base and I could not see the runway but our vector was inside the FAF. We probably should have said no to the super tight vector. Once again; we made it work but should not have had to fly a heavy cargo plane that aggressively.

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Original NASA ASRS Text

Title: B767-300 flight crew reported various anomalies with the FMS.

Narrative: So we had multiple strange events on cruise and descent. During cruise we noticed an execute light on the FMS. Neither of us was sure what the execute light was for and the Captain scrolled through the FMS pages to try to figure out what wasn't executed. We were in normal cruise as I recall and had recently stepped to FL 370. Somewhere through the scrolling of pages the plane went into continuous thrust mode and started slowing down to drift down speed. Neither of us executed the drift-down. Neither of us even attempted to get drift down speed and altitude during the short flight to ZZZ. So I was not the designated Flying Pilot for the flight but I had control at the time and overrode the auto-throttles to keep us at cruise speed while the Captain attempted to fix the FMS and get us back to Econ cruise speed. Nothing happened but we were told by maintenance after the flight that the aircraft had done something similar on a previous flight. Secondly; on the descent while on the VNAV path the Captain extended the speed brakes and we got an 'Unscheduled stab trim caution and an autopilot caution.' No one touched the electric or alternate trim and the autopilot stayed engaged. We did not notice any changes in the aircraft. When I was about to run the QRH the message went away and we continued and mentioned the situation to maintenance. And on the ATC side; not to be whining; but we did get the tight visual approach inside the final approach fix. The Captain went off automation as the glideslope would not have been able to be tracked on the AP. We started out high and then ended up low on the glideslope with a correction. We were able to make the 1000 foot stable gate on the glideslope just barely. However I am noting these things because it is my opinion that ATC needs to stop treating heavy Boeing 767s carrying cargo like we are CRJs capable of making aggressive last second maneuvers in the landing pattern. I realize that some of us more aggressive pilots can use skill to make things happen; but we should not have to. ATC needs to treat us like every other heavy; low maneuvering jet. This sort of situation could lead a less experienced pilot to make a mistake.For the drift-down situation; I felt we did a good job preventing the situation. No one freaked out or did anything radical and we corrected the problem. The unscheduled stab trim was handled without any major issues. However we are occasionally getting these strange cautions on the auto-flight system that pop up and then disappear. We shouldn't be getting them at all if the plane is not having any problems. It makes you have to decide whether you run a QRH or not and whether you need to write it up or not. It also creates a distraction and a feeling of distrust on the aircraft. This is not a good feeling; especially considering recent events. As to the visual approach; the Captain probably could have said 'no' to the tight vector to final. We were in a left downwind to base and I could not see the runway but our vector was inside the FAF. We probably should have said no to the super tight vector. Once again; we made it work but should not have had to fly a heavy cargo plane that aggressively.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.