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 and the REALISM setting is 5 or higher (Virtual AGC Mode).
The intention is that the failures will never be immediately or inevitably fatal, but will keep you on your toes and may require you to abort or change the mission to compensate. Some failures will kill you if you don't take such actions (e.g. manually deploying parachutes which fail to deploy automatically).
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.
The LET auto jettison may fail, requiring you to jettison the tower manually. The LET jettison motor may fail, requiring you to jettison the tower manually with the abort motor. Automatic separation of the SII stage from the SIC may fail, requiring you to separate manually.
Random lights on the Caution and Warning System will fail.
Any of the TWR JETT and SM JETT switches may fail, though only one of each type will fail at any time as having both fail would be fatal. If one of the two redundant switches doesn't function, use the other.
The apex cover deploy, drogue deploy and main chute deploy may fail randomly. You will have to deploy them manually.