For the exact answer to Garfield's question, FAR part 25 section 1001(a) says:
"(a) A fuel jettisoning system must be installed on each airplane unless it is shown that the airplane meets the climb requirements of §§25.119 and 25.121(d) at maximum takeoff weight, less the actual or computed weight of fuel necessary for a 15-minute flight comprised of a takeoff, go-around, and landing at the airport of departure with the airplane configuration, speed, power, and thrust the same as that used in meeting the applicable takeoff, approach, and landing climb performance requirements of this part."
Part 25.119 & 25.121(d) refer to climb performance in the landing configuration, with the most restrictive (25.121d) being with one engine inop but the normal all-engines operating landing configuration.
In other words, aircraft climb performance at max gross weight (less 15 minutes of fuel burn) with one engine inoperative and normal landing configuration determines whether a fuel dumping system is required or not. If the plane can meet the performance criteria, no fuel dump system required. If it can't, it's gotta have a fuel dump system.
As for the fuel dump system itself, it has to be able to dump enough fuel in 15 minutes for the aircraft to meet the above requirements. Obviously, by dumping longer one can get the aircraft weight down even further for landing.
Additionally, it must be shown that any fuel dumping system meets these requirements:
1) The fuel jettisoning system and its operation are free from fire hazard;
(2) The fuel discharges clear of any part of the airplane;
(3) Fuel or fumes do not enter any parts of the airplane; and
(4) The jettisoning operation does not adversely affect the controllability of the airplane.
The 727 is the only U.S. manufactured aircraft that I know of that has a fuel dump system and rear mounted engines. Notably, the fuel dump outlets on the outboard trailing edge of the wings was well outboard of the engines, and on the -100 model was actually slightly behind the engine intakes. All aircraft with wing-mounted engines have the dump point well outboard and behind the wings since they're also on the outboard trailing edges.
Jim