Random Failures
Project Apollo has an option to create random failures for your scenario. This is enabled by default if you don't specify the APOLLONO in the scenario file.
Failure Modes
Launch Failures
The center engine on the SIb, SIC and SII stages may randomly shut down early. This may or may not require a launch abort or a different mission profile depending on when in the launch it occurs: with a Saturn 1b this may not leave enough fuel to reach orbit, and with a Saturn V it may not leave enough fuel to reach the Moon.