Simply taping the connection could still result in a short (that's what sparks mean) happening under the tape, which is 1) a serious fire hazard; 2) a good way to trip your circuit breaker a lot; and 3) potentially damaging to the computer. If you absolutely HAD to do this, you would need to make sure each wire was individually wrapped, so that they could not touch each other, then tape the whole thing up. BUT, if you can afford a new one, i STRONGLY suggest you go this route, even someone experienced with electronics would have a hard time accomplishing this repair safely.
Make sure you always remove the cord by grasping the hard plug on the end, not by pulling on the cable itself. This is how cords and cables get damaged- altho i will admit Apple doesn't use very durable cables. I've had a mouse and an iPod cable meet their doom the same way, and i'm pretty careful.
edit: after re-reading the thread, it sounds like jim's suggestion of applying extra coating would serve nicely, since this is a non-removable connection. Buy a new one and coat it. Be careful using adhesives tho, because some actually melt the plastic to form a bond-- and of course, if the plastic melted deeply enough in this situation, it could break down the coating on the individual wires, re-bonding the entire thing with those wires touching.
paul