Continuity always needs to be right, but sometimes there are deliberate errors. Of course you need a good motivation to do one of these, but I think it's great when it gets pulled of right. One of my favourite ones happens in the fifth series of Doctor Who, in the episode "Flesh and Stone".
Continuity Blog
This is my blog. I write about things I like: playing around with continuity and nice cuts. I don't use this blog to point out continuity errors, but rather to celebrate when continuity is used in an interesting way.