One of the pilots described on Facebook how a plane rented from Damojh Airlines had dropped off-radar completely some eight years ago, prompting key crew members to be suspended.
Mexican authorities say they will carry out a safety audit of the company.
Separately, it was revealed that 10 priests were among the crash victims.
Three women survived the crash near Havana airport - Cuba's deadliest aviation disaster in more than 30 years.
One of two "black boxes" that hold key flight data and information about what happened to the plane has been recovered and is said to be in good condition.
Cuban authorities have launched an investigation into the crash, as rescuers continue to comb through the wreckage site some 20km (12 miles) south of the Cuban capital.
What were the safety complaints?
Allegations of previous safety complaints have emerged against the Mexican Damojh company, which leased both the Boeing 737 and its crew to Cuba's flagship state Cubana airline.
The head of Guyana's civil aviation body, Cpt Egbert Field, told the Associated Press news agency the same plane - which was nearly 40 years old - had been barred from using Guyanese airspace last year after authorities found its crew were overloading luggage on flights in Cuba.
In one instance, the news agency reports, Guyanese authorities had discovered suitcases stored in the plane's toilets.
Image copyright AFP Emergency personnel work at the site of the accident on 18 May 2018.
Image caption The plane crashed in a field near Havana international airport
Meanwhile, a retired pilot for Cubana wrote on Facebook that another plane rented by his airline from the same company had briefly dropped off radar for unspecified reasons while over the central Cuban city of Santa Clara in 2010 or 2011.
The captain and co-pilot of that flight were later suspended for "problems and serious lack of technical knowledge," said Ovidio Martinez Lopez, who worked for Cubana for more than 40 years.
He said "many flight attendants, flight attendants and flight safety personnel" had refused to fly on certain Cubana planes over the years.
Another pilot who used to work for Damojh told Mexican newspaper Milenio he had complained about a lack of adequate maintenance of planes.
"I experienced several incidents at this company, like engine failure or the electrical system went when we took off from Mexico on one occasion", Marco Aurelio Hernandez was quoted as saying.
The company has yet to comment on the allegations.
Who were the victims?
Cuba's transport minister said on Saturday that five children were among the victims. Adel Yzquierdo also updated the official death toll to 110, and listed the nationalities of the victims:
99 Cubans
Six Mexican crew members
One Mexican tourist
An Argentine couple
Two passengers from the Western Sahara (a disputed territory annexed by Morocco after Spain withdrew in 1975)
Also among the dead were 10 evangelical priests and their spouses who had been meeting in Havana for several days and were returning to their homes in Holguin province, where the flight was destined to land.
"On that plane were 10 couples of pastors. Twenty people. All of the Nazarene Church in the eastern region," confirmed Maite Quesada, a member of the Cuban Council of Churches.
Image copyright Reuters Relatives of victims of the Boeing 737 plane that crashed yesterday react as they leave the Legal Medical Institute in Havana, Cuba, 19 May 2018.
Image caption Victims' relatives have been helping authorities in Havana to identify their loved ones
The Argentine couple have been named by their government as Dora Beatriz Cifuentes and Oscar Hugo Almaras, both in their 60s.
Several victims' relatives have travelled to Havana to help identify the deceased.
Meanwhile, the three survivors remain in critical condition with serious burns.
"My daughter is a fighter, she's strong, she'll save herself," the mother of a 23-year-old survivor, Amparo Font, told Reuters news agency.
Mexican authorities say they will carry out a safety audit of the company.
Separately, it was revealed that 10 priests were among the crash victims.
Three women survived the crash near Havana airport - Cuba's deadliest aviation disaster in more than 30 years.
One of two "black boxes" that hold key flight data and information about what happened to the plane has been recovered and is said to be in good condition.
Cuban authorities have launched an investigation into the crash, as rescuers continue to comb through the wreckage site some 20km (12 miles) south of the Cuban capital.
What were the safety complaints?
Allegations of previous safety complaints have emerged against the Mexican Damojh company, which leased both the Boeing 737 and its crew to Cuba's flagship state Cubana airline.
The head of Guyana's civil aviation body, Cpt Egbert Field, told the Associated Press news agency the same plane - which was nearly 40 years old - had been barred from using Guyanese airspace last year after authorities found its crew were overloading luggage on flights in Cuba.
In one instance, the news agency reports, Guyanese authorities had discovered suitcases stored in the plane's toilets.
Image copyright AFP Emergency personnel work at the site of the accident on 18 May 2018.
Image caption The plane crashed in a field near Havana international airport
Meanwhile, a retired pilot for Cubana wrote on Facebook that another plane rented by his airline from the same company had briefly dropped off radar for unspecified reasons while over the central Cuban city of Santa Clara in 2010 or 2011.
The captain and co-pilot of that flight were later suspended for "problems and serious lack of technical knowledge," said Ovidio Martinez Lopez, who worked for Cubana for more than 40 years.
He said "many flight attendants, flight attendants and flight safety personnel" had refused to fly on certain Cubana planes over the years.
Another pilot who used to work for Damojh told Mexican newspaper Milenio he had complained about a lack of adequate maintenance of planes.
"I experienced several incidents at this company, like engine failure or the electrical system went when we took off from Mexico on one occasion", Marco Aurelio Hernandez was quoted as saying.
The company has yet to comment on the allegations.
Who were the victims?
Cuba's transport minister said on Saturday that five children were among the victims. Adel Yzquierdo also updated the official death toll to 110, and listed the nationalities of the victims:
99 Cubans
Six Mexican crew members
One Mexican tourist
An Argentine couple
Two passengers from the Western Sahara (a disputed territory annexed by Morocco after Spain withdrew in 1975)
Also among the dead were 10 evangelical priests and their spouses who had been meeting in Havana for several days and were returning to their homes in Holguin province, where the flight was destined to land.
"On that plane were 10 couples of pastors. Twenty people. All of the Nazarene Church in the eastern region," confirmed Maite Quesada, a member of the Cuban Council of Churches.
Image copyright Reuters Relatives of victims of the Boeing 737 plane that crashed yesterday react as they leave the Legal Medical Institute in Havana, Cuba, 19 May 2018.
Image caption Victims' relatives have been helping authorities in Havana to identify their loved ones
The Argentine couple have been named by their government as Dora Beatriz Cifuentes and Oscar Hugo Almaras, both in their 60s.
Several victims' relatives have travelled to Havana to help identify the deceased.
Meanwhile, the three survivors remain in critical condition with serious burns.
"My daughter is a fighter, she's strong, she'll save herself," the mother of a 23-year-old survivor, Amparo Font, told Reuters news agency.