Moving wordpress to different URL

Hi,
I have a wordpress instance running on my Linux CentOS box here, at the URL mydomain.com/wordpress.

I wanted to get rid of the ‘wordpress’ bit, so took the coward’s way and did it just by leaving it where it is, but copying index.php and .htaccess one level up. Remarkably, all of my posts which were already there, are available at the correct URL: mydomain.com/?p=123, for example.

However, a couple of issues have arisen. One is that if I go to a post which I have already written and click on a link in that post, which points to a previous post, then it goes to mydomain.com/wordpress/?p-<postnumber>. The link still works, but I’m guessing that this is the bit about search and replace which is in the Codex? Is this safe to do, using the script here? I downloaded that script and was about to launch it, but got cold feet.

Issue number two is that if I start a new post, save the draft and then do ‘preview’, it gives me a 404, since it looks in /?p=123&preview=true. If I add ‘wordpress’ before the slash, I can see my preview, but without it, I get ‘this is somewhat embarrassing..’

How can I fix this?

Thank you.