This paper identifies potential weaknesses and challenges of hydrogen fuel cell systems as main energy provider for electrified aircraft propulsion and presents potential solutions. The general design, operating principles and main characteristics of hydrogen-fuelled low-temperature polymer electrolyte membrane fuel cell systems (PEMFCSs) are described. The safety assessment process in aviation according to Aerospace Recommended Practices ARP4754A and selected methods according to ARP4761 are introduced. The functions of fuel cell systems in electrified aircraft powertrains are analysed in functional structure trees on aircraft, powertrain and fuel cell system level. By means of a Functional Hazard Analysis (FHA), potential malfunctions and their effects are investigated and their severity is evaluated. Critical failure modes are identified and requirements for acceptable failure probabilities are stipulated. Solution options to mitigate failure effects are stated. The results of the mentioned analyses reveal design challenges associated with the application of fuel cell systems in electrified aircraft propulsion, for instance, concerning functional independence as well as solutions for cold start conditions, heat transfer and lightweight design. Furthermore, safety challenges arise due to the utilisation of cryogenic hydrogen as fuel and the high amount of electric energy.