In the movie Skyfall Shouldn't Q like connect Silva's computer to a secure line or something, considering that he was a known cyberterrorist? Isn't there any sort of internal protocols for the networking system?
There is no proper reason whatsoever for him to link the unsecure device retrieved from an enemy to the network of MI6. The usual approach would be to treat it with the highest level of suspicion and analyze the hardware and contained data in a secure isolated environment, and Q should have known that, considering that he is supposed to be a genius IT specialist.
This is a trope called the Idiot Ball (warning: TvTropes link!):
If you are looking for a reasonable in-world explanation, one could come up with the following reasons for his mistake:
Still, that was a very stupid thing to do and for me was one of the biggest facepalm moments in the movie.