■ While being vectored to final, ATC gave us a heading with clearance to intercept the localizer course.... The Pilot Flying instructed me to arm the localizer. I responded that we needed to be in NAV before arming the localizer because of the strong overshooting winds (42 knots at 4,000 feet MSL). The Pilot Flying selected NAV and then I armed the localizer for him as he requested a cleanup of the FMS. I saw that NAV/LOC had both armed and went heads down to clean up the FMS. I looked up to see the airplane starting a left-hand turn away from the runway and immediately instructed the Pilot Flying to turn back towards the runway. I also glanced at the PFD and noticed we were now in Heading mode (no NAV or LOC armed/selected). The result was an overshoot of the final approach course. I instructed the Pilot Flying to be aggressive in getting back over to final as we received a follow-on intercept heading from ATC.

Selecting NAV and then LOC was needed, but the FMS should have been cleaned up prior to selecting these modes. By selecting them first and then cleaning up the FMS, I may have inadvertently put us in Heading mode. Also, the First Officer needed to monitor our lateral mode and be ready for any reversions or changes to that mode. When the plane attempts to do something we don't want it to do, the Pilot Flying needs to turn the autopilot off immediately and put the airplane in the correct position.

FMS clean up should take place well before the intercept to final and as Pilot Monitoring, I should have been more aggressive in making that happen earlier.

■ Center gave us a clearance to descend to FL330 and fly direct to a fix. I pushed the ALT (Altitude) button to descend in Managed Descent mode then typed in the clearance to fly directly to the fix. I then checked the crossing altitude in the FMC for the arrival. Four minutes later ATC called and asked if we were descending.

While on a heading, the A320 will not descend in Managed mode, so the aircraft stayed at FL350. If I would have programmed the FMC first, then pushed the ALT button, the aircraft would have descended in the Managed Descent mode. I also could have pulled the ALT button and descended in Open Descent mode or in the Vertical Speed mode. Our procedure is to check the FMA's once you have made an input to the auto flight system. I did not do this.

■ Cleared to descend to 2,000 feet, we were turned towards final by Approach Control. [We were] then given another turn to intercept and cleared for LOC 31 approach, maintain 2,000 until QUENE. The final intercept vector was going to bring us well inside QUENE, so I extended off FABRY (FAF), armed the LOC, and switched to ARC mode on my NAV Display to monitor DME in order to identify abeam QUENE, and to monitor LOC capture.

After passing abeam QUENE at 10.3 DME, with LOC capturing and FABRY (FAF) next, I called for the First Officer to set and arm 600 feet which was our MDA, and I initiated descent out of 2,000 feet. It was a busy time now completing final configuration for landing, slowing down, and completing the Landing checklist. I had left ARC mode on my NAV Display. I was not aware that the First Officer was also in ARC mode, thus neither of us were watching the "football" on the NAV Display which was now our only protection for crossing FABRY at 1,700 feet, the published altitude at the FAF.

On the LOC and descending, we were told to contact Tower. Before Tower contact was made, the First Officer figured it out and said "Hey, we're really low. We need to climb." The altitude was approximately 1100 feet, or 600 feet low, a couple of miles outside FABRY. I realized what I had done and climbed back to 1,700 feet just as we reached FABRY. Tower…issued a low altitude alert. After FABRY a normal descent to landing was made. We were IMC until about 1,100 feet…. We did not get a GPWS warning.

This one scared me. I fully grasp that being that far (600 feet) below a hard altitude on an approach will get you killed in many places. I honestly don’t think complacency was our issue. I was not cavalier about this approach and neither was the First Officer. The approach was thoroughly briefed. One thing I did not specify though was who would have what (ARC or MAP) displayed on the NAV Display. We needed both for at least a short while, in order to see DME.

As pilot flying, it was my responsibility to see that I had displayed what I needed to shoot this approach in accordance with our procedures. I made a mistake when I did not go back to MAP mode after passing abeam QUENE. If MAP mode had not been available, then I would have had to set 1,700 feet for FABRY, followed by 600 feet for the MDA after passing FABRY. If MDA is set outside the FAF, then I MUST be in MAP prior to the FAF. I am fortunate to have had a good First Officer who regained situational awareness before I did.

■ After being cleared for the ILS…under visual conditions, at some point the aircraft came out of Profile Descent mode or it was deselected. The aircraft descended below the Profile Descent path. At about 12 miles from the field, we elected to level off at approximately 1,500 feet AGL. We had the field visually and…the rest of the approach was flown without issue.

The altitude that was set in the Altitude Select window was the Decision Height. The airplane was trying to descend early to the Decision Height because Profile Descent was not engaged. A better check of the Profile mode would have stopped this from happening. We also should have left the last assigned altitude in the Altitude Select window. This also would have stopped the plane from descending early.