Does it matter where my academic website is hosted, for issues of intellectual property? Say I am a British academic, who happens to have a blog, where I comment on my research and other people's research. Naturally, I do not want to infringe copyrights on any type, including intellectual property (IP). Yet, it seems that the IP law is "more loose" in the US than in the UK. In effect, whereas the US law is defined on positive terms ("this is what you cannot do"), the UK is defined on negative terms ("this is what you can do").

Just for the sake of minimizing potential, unintended infringement of IP copyrights in my blog, should I register my website in the US, or is that irrelevant?
I can hardly see how writing your own comments on someone else's published work can come close to any sort of copyright infringement. Obviously, you would not re-publish someone else's papers in your blog? Small quotes are allowed in the UK under fair dealing exception (aka fair use). IANAL, but I would be surprised if it's any different in the US. 

Obviously, if you republish someone else's papers in full, this is anything but a blog.