I think the amount of research you put into something depends on the genre of the story. If you're doing, say, a conventional murder mystery, you're definitely going to want your facts straight.

If you're doing sci-fi, better get the laws of physics right or people will nitpick it to death (yeah, I know, there are some expections to the rule, but the theories should at least be sound.)

If you're doing a Harry Potter-style fantasy, there aren't going to be many facts you'll want to use, but you'll still have to work within the rules of your own universe, however illogical they may be. Even Discworld has rules.

I personally research facts only when they are absolutely crucial to the story's plot. Otherwise, I tend to just let my imagination run with the idea I had and let the characters develop the plot.

I believe there's a hero in all of us that keeps us honest, gives us strength, makes us noble, and finally allows us to die with pride, even though sometimes we have to be steady and give up the thing we want the most. Even our dreams. -- Aunt May, Spider-Man 2