While the nylon thread can stretch, it can also be heat shrunk (very carefully, lest you break something). There is a big difference between monofilament and regular thread, however. The monofilament is stiff, almost like fine stainless steel wire, and tying knots in it is a real pain. However, it looks much finer than it is, which makes it very attractive on smaller scales.
Every time I rig with monofilament I swear it will be the last time. But the results look so good I end up using it again.
Regular multi-strand thread can certainly depict rigging well. If it is thin enough (say 8 mil) your eye will have a hard time seeing the filaments, though. A good gray 8 mil is hard to find, though.
Biggest problem I see in finished ship models is using too large a thread, and too high a contrast color. Black or white does not look realistic- a medium grey is usually a better color, and the lower contrast calls less attention to the rigging. Rigging should be subtle. Note that it does not show up in many pictures, depending on the lighting and exposure used.