Presumably they meant a program being discovered to be wrong before the computer was actually launched. And meant literally building a whole new computer, not just recompiling a program.
For the Apollo Guidance Computer, changing the program meant manually re-weaving wires through or around tiny magnet rings. A good part of the cost of the computer was the time spent painstakingly weaving the wires to store the program.
Pardon me, but why would you have to re-weave wires around magnetic rings? The magnetic rings are for storing data; the whole point is that you can change the data without rewiring the memory. If you have to re-wire permanent storage (e.g. program storage), that's equivalent to creating a mask ROM, which is basically just two funny-shaped sheets of conductor. There's no need for magnetic rings.
Only if the bug was caught after the computer had been assembled for the mission. For development, they used a simulator. Basically, a cable connected to a mainframe, with the bigger computer simulating the signals a bundle of core rope would produce.
Yeah, though to be fair, some of the programs Apollo ran were on hand woven ROMs, so I may be making too fine a distinction. The program itself was built, not compiled. It if we are comparing with today, it would just be installed, not constructed.