I suggest reading the Apollo 13 node before continuing, or at least watching the movie. For those who haven't, the long and short of the mission follows. Skip the following section as appropriate.
Background
On 11 April, 1970 the Saturn V rocket carrying astronauts James Lovell, Fred Haise and Jack Swigert, not to mention command module Odyssey, lunar excursion module Aquarius and 450 tonnes of propellant, lifted flawlessly from Cape Canaveral, Florida. Destination was the Frau Mauro Highlands near the Sea of Tranquility. Aside from a hiccup with one of the second stage J-2s, the ship functioned well until just short of 56 hours into the mission.
The Apollo vehicles carried cryogenically-stored liquid oxygen and hydrogen. These two substances, when stored in zero gravity, tend to separate into areas of varying densities. This could cause the 'tank level' sensors to return a false reading on how full the respective tanks were. To avoid this happening, the tanks were 'stirred' once a day to even out the density of the fluid, using a pair of small internal fans.
The problem occurred because of - in the words of the NASA review board - "an unusual combination of mistakes, coupled with a somewhat deficient and unforgiving design." The heater assembly used on the oxygen tanks contained a thermal cutout switch, to shut the heaters off at a certain temperature. Unfortunately, several years after the original specifications for the tanks were supplied to manufacturers Beech Aircraft Corporation, the power specification was amended from a 28v DC supply to 65v DC. The thermal cutout switches were not replaced in line with this change, nor was this fact picked up by BAC or NASA.
This in itself would not have caused problems, since the change occurred after the tank in question had been manufactured, and after the mission it was intended for had completed. However before the tank could be fitted to its designated service module, it was damaged. The tank was held back for repair and another tank was used in its place; the repaired tank would then be used in Apollo 13's service module but the thermal cutout switches were not replaced to reflect the higher voltage that they would be supplied with.
No damage would occur to the switches until they were operated but when they did, at over twice their rated voltage, an electrical arc caused them to exceed their temperature tolerances and permanently weld themselves closed, allowing the heater to continue operating unchecked. The heater exceeded 1000° F at times, since it was required to operate for 8-hour periods. Of course no-one noticed this, since the normal operating temperature range of the oxygen tank was -300F to 80F and the gauges didn't provide readings outside this range. This excessive temperature probably destroyed the Teflon insulation on the cables supplying the fan motors with power. When the fans were operated during the cryo stir, the cables short circuited and ignited the insulation, in turn igniting the oxygen.
Then No.2 oxygen tank burst.
The service module severely damaged and venting oxygen, the command module had to be shut down to remain usable for re-entry. The moon landing mission was scrubbed in fairly short order as it was impossible with the damage sustained; the new mission was to get the astronauts back. In probably-insulting brief, this was done by using the lunar module to provide power, oxygen and propulsion to the command module to get it back to Earth. This was not without its difficulties, not least having to fly for a good portion of the return journey without a guidance computer, having a frozen command module and no air conditioning, but I will again point the reader in the direction of the Apollo 13 node, (particularly scuzzy's writeup, which has excellent detail on the fault with the oxygen tank).
Towing Bill
Sooo, it's now April 17, 1970 and Apollo 13 splashes down in the Pacific Ocean just after midday. Everyone's pretty pleased with themselves and don't even notice their rocketing (hah!) blood pressures or the amount of cigarettes and coffee they've consumed over the last week. Yup, life is good for NASA. Never before had a failure been such a triumph.
A short time later North American Rockwell, designers and manufacturers of the Apollo command and service modules, received an invoice from Grumman Aerospace Corporation, designers and manufacturers of the lunar module. Now, since being respectively handed the top and bottom/second prizes in space manufacturing contracts, something of a rivalry had arisen between the two. It was clear that Grumman's LEM had saved Apollo 13's day, and the joke invoice detailed $312,421.24 of charges to Rockwell for services rendered towing their crippled command and service modules back to Earth:
ITEM QTY Unit Description Unit Price
1. 400,001 MI Towing, $4.00 first mile, $1.00 each additional mile $400,004.00
Trouble call, fast service
2. 1 ??? Battery Charge (road call + $.05 ???) 4.05
customer's jumper cables
3. 50# # oxygen at $10.00/lb 500.00
4. 1 sleeping accommodations for 2, no TV, air-conditioned,
with radio, modified American plan, with view NAS-9-1100 prepaid
5. Additional guest in room at $8.00/night (1) Check out no
later than noon Fri. 4/17/70, accommodations not guaranteed beyond that time 32.00
6. Water no charge
7. Personalized "trip-tik", including all transfers, no charge
baggage handling, and gratuities
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sub-total $400,540.05
20% commercial discount + 2% cash discount (net 30 days) (-) 88,118.81
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total $312,421.24
No taxes applicable (government contract)
Pretty damn funny. Apparently Sam Greenberg, the Grumman employee who made others aware the invoice existed (it was made up by people working at Grumman's Flight Control Integration Lab) was fired for doing so. For about two hours. Then Lou Evans, president of Grumman, reinstated him, signed the invoice and it was sent out. Rockwell responded the same day in a press conference, where a spokesman deadpanned that Grumman, before issuing such an invoice, should remember that Rockwell had still not received payment for shipping four of their LEMs out to the moon.
The invoice: http://myweb.accessus.net/~090/as13/as13bill.png | 
