I've always been able to download GOG games without any problems, but I do hear about others having problems sometimes. Usually the solution is to try the GOG downloader if you haven't tried that, and if that doesn't work then try using different web browsers to do the download. The Witcher is a very large download so it can sometimes have problems. Failing that, repeated tries will often do the trick.
One nice thing about downloading with the browser is that it's split up into several chunks, so you can get some of them to finish properly and then just re-download the ones that didn't, rather than having to download the whole game again.
EDIT: Forgot to mention that some internet provides may throttle you after you've downloaded enough stuff. This is annoying, but it's usually done per month so if you start your download at the beginning of a cycle it will hopefully work. Then, since GOG games are DRM-free, you can just keep the installer files somewhere and reinstall from them as many times as you like without having to download anything again.
Post edited October 20, 2014 by Waltorious