calibre is a very rapidly evolving piece of software, with weekly releases. As a results bugs are inevitable. We rely on calibre's users to report these bugs, so that they can be fixed as quickly as possible. To report bugs use the calibre bug tracker. Note that you will have to register for a free account first.
When reporting bugs please include as much information as possible, as that makes it easier for us to identify the source of the problem. Remember that calibre is developed by volunteers in their spare time, so by taking these steps, you are helping to ensure that as much of that time as possible is spent actually coding as opposed to doing administrative tasks like closing duplicate bug reports.
If you are including some sensitive data in your bug report like a copyrighted book or a debug log, mark the bug as "private", then the data will not be visible to all. You can do this by finding the location where it says "This report contains Public information" in the top right area of the bug's page and clicking the yellow icon next to it.
You can also use the bug tracker to request new features. To mark a bug report as a request for a new feature just add [Enhancement] to the subject. Please remember that calibre is a highly complex piece of software with millions of users, as such, the priorities of calibre's developers may not match your own and your feature request may well be ignored. Since calibre is open source, one sure way to get your feature request more attention is to implement it yourself and attach the patch implementing it to the bug report.
Note that the bug reporting site is currently incompatible with some version of Internet Explorer, so if you have trouble try using an alternate browser like Firefox, Chrome or Safari. Or try clicking the "Compatibility mode" button in Internet Explorer.