Fill out more stuff here about other aspects of Cydia that may be interesting to developers.
TheiPhoneWiki has a list of Cydia error messages and what they mean.
Developing tweaks for Cydia
You can contribute advice and information here about making extensions for Cydia.
As of Cydia 1.1.19, you can build extensions (tweaks) for Cydia to add new features and modify existing ones.
Cydia's code is open, so you can look at it to help you. Here is also a tip from saurik though: "FWIW, I would recommend dumping headers for various reasons; my code uses a bunch of C++ templates and macros, it wasn't designed to work like a library so I don't separate interfaces from implementation as separate files in the general case, and frankly: dumping is a workflow that makes sense and is easily repeated; honestly, I, even as myself, would actually dump headers rather than scavenge them."
Contributing to Cydia
If you're interested in contributing improvements to Cydia, the process is similar to contributing to WinterBoard. The first step is to get in contact with saurik and Britta (preferably via IRC in the #cydia channel on irc.saurik.com - see How to use IRC) and discuss the idea you have in mind, or explain your skills and ask for suggestions about what to work on.
(If you'd like to help with design, please don't start by showing Photoshop mockups - they generally can't be integrated in a practical way, since they usually don't address all of the constraints that Cydia is working under. Instead, it's helpful to start by explaining that you'd like to help with design, and show some examples of work you've done and what kind of design you like to do.)
The most likely next step is that saurik and Britta will have some feedback for you on your idea, or some suggestions for things you could work on. Making improvements to complex software is usually an iterative process - in other words, it takes several rounds of discussion, adjustments, and improvements to get something that works well. (For example, Surenix worked with saurik on the Cydia Substrate icon, and he explained in a JailbreakCon talk that it took several revisions and a lot of discussion to come up with a great icon.)
After discussing your idea and working on it, saurik usually doesn't need a full code patch from you; if you can provide a proof of concept with a bit of useful code (or a bit of useful HTML/CSS), he can adapt that into the codebase in a way that makes sense for long-term maintenance.
If you'd like to read Cydia's code, it's useful to note that the code is formatted/organized in a way you might not expect - saurik uses a command-line text editor called vim, and he uses a feature called "folds". Check out this video and this one too to learn more if you like. You don't have to use vim folds to read Cydia's code, it just helps to know that to understand how the code is formatted.