A few points on this one:
Most P&S cameras don't have a mechanical shutter or iris so there are no moving parts and hence the number of images they can capture is practically unlimited (think how many "images" a digital video camera shoots in it's lifetime!)
Every Canon I've ever used has it's own very distinctive shutter noise, so it may be that the 300D (one of Canon's first DSLRs) has always sounded that way.
To answer your question there are a few disadvantages to a worn out shutter:
Increased noise (and possibly slower mirror movement hampering rapid fire).
Increased likelihood of the shutter giving up completely with no warningin the middle of a shoot.
Loss of high shutter speeds. Basically the first and second shutter curtains can get out of sync, giving you unpredictable exposure times, the faster the shutter speed the more variation.
The last one is important, when I've had shutters go the high speeds 1/20004000 & 1/40008000 went first. Basically the first and second curtains were no longer in sync resulting inthe 1000 - 2000 range became unpredictable, giving me a lotbit of black framesa warning it was going to fail.
Having said that, if it's still working then it's still working. The shutter shouldn't affect image quality - provided it's open at the right time! The sensor should be unaffected as it has no moving parts, if it fails I would expect an outright failure not a gradual degradation, though the number of hot/dead pixels may increase over time. It is possible, though very unlikely, for the sensor to have shifted out of alignment (which could, incidentally result in soft images). A knackered mirror assembly might affect the viewfinder image and AF (since light is directed onto the AF sensor via a second mirror which hangs down from the main one).
At the end of the day, a shutter replacement on a 300D would almost certainly cost more than a camera upgrade so your friend might as well shoot it 'till it dies!