B737 Next Generation Undifferentiated
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 190
Situational Awareness
ATC Issue All Types; Conflict Ground Conflict; Less Severe
Air Traffic Control Issued New Clearance
Human Factors; Procedure
During International departure from MMSD (SJD); SJD Clearance Delivery; Ground; and Tower were all being conducted on frequency 118.9 by one Air Traffic Controller; on one of the busiest (traffic) days I've seen at SJD; with landings and departures being conducted to Runway 34.  We started and taxied uneventfully (although radios were very congested) to Runway 34 and were #3 to takeoff with several arrivals. While eventually holding short of Runway 34 number 1 to go; Company called for clearance; and Tower replied for us to hold short of the runway. It was very obvious he was task-saturated and getting confused running three frequencies. As well; the Controller reverted to Spanish working some of the other local traffic at times. Another carrier then called for clearance and the Tower Controller finally pushed them to a separate clearance frequency. During all of this; as aircraft landed; the Controller told each to bypass Taxiway C (NOTAM'd closed) and clear at Taxiway D. As we held #1; Air Carrier Y landed and rolled out on the runway; with another aircraft five to seven miles out; Tower asked if we were ready to go; which we replied affirmatively. Tower then said; 'Company # cleared for takeoff Runway 34; do not delay; traffic on final.' My FO replied; 'Cleared for takeoff Runway 34;' but as we took the runway; I noticed the previous Air Carrier Y had begun clearing at Taxiway C (Tower said something to him in Spanish) and then turned back nose pointed west then back north on Runway 34. I watched all this transpire and never pushed the power up to take off; but set the brakes; telling my FO we weren't going anywhere until the runway was clear and we were re-cleared for takeoff. Once the runway was cleared by the previous carrier on Taxiway D; and cleared for takeoff again by Tower; we departed uneventfully. I'm not sure how close the traffic on final got; but once we were safely away from SJD and at altitude; I sent Dispatch a message to forward to Company ATC and Safety personnel; and any follow-on Company arrivals to make them aware of the ATC safety issues happening at SJD. Had the visual conditions been worse; a Ground collision on takeoff would most certainly have resulted.Our vigilance today; along with some good visual lighting conditions; probably prevented a very dangerous situation from happening (which I honestly believe any other Company Pilot would have also seen and prevented in the same circumstances). SJD ATC was definitely in over their heads today and very task-saturated.
Cabo Tower needs to pass the Ground and Clearance duties to other frequencies on very busy travel days.
B737 flight crew reported they were cleared for takeoff with an aircraft still on the runway because MMSD ATC was overwhelmed with traffic with one Controller working three frequencies.