Trac is the place to follow along with the development of WordPress. You can track changes in the Timeline section of this site. There is also an RSS feed and a mailing list (we call it the firehose) for those interested.
If you are looking to submit a bug report, please head on over.
You don't need to subscribe to the mailing list to be kept updated. You will automatically receive notifications for tickets you have reported or participated in. If you would like to receive notifications for a ticket, simply click "Watch this ticket" to star it.
You can browse the source here, but you probably want to check out WordPress using Subversion.
If you have encountered a security issue that isn't addressed in a released version of WordPress, please contact security at wordpress.org with detailed information. For more, see our Security FAQ in the handbook.
There are many ways to contribute to WordPress. We have a detailed contributor handbook to help get you started. If you want to get started quickly, test a patch, or grab a bug and see if you can reproduce the problem it describes. Don't miss the PHP and JS unit tests — and if you like writing unit tests, there are some tickets that could use them.