If you do a conversion without dithering, you run a slight risk of hearing quantization (math) errors. When the division of bits isn't clean, you end up with what are called LSB's (least signifigant bits) or "extra" bits. Dithering allows the LSB's to be dealt with so we don't hear them(honestly, you may not without dithering but if done right, the pro's outweigh the cons, for me).
If you use the right dithering software, it is almost transparent. The amount of "noise" added in to offset quantization errors is at a volume thats basically inaudable by the human ear. I would always dither when changing from a 24 to a 16. I would rather not take a chance. Dithering, for what we do, should only happen once in the whole process. If you use a crappy program, yes, you will hear it.
http://www.voxengo.com/product/r8brain/
r8brain free is probably the best free utility to do sample rate conversion and dithering. There are better programs but they get into some serious dough.
You may never have a problem or you may always have a problem depending on which way you go and what hardwaree software yu use. I like to play it safe myself. This is totally different for different editors though so make sure you do your homework.
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