This point of view holds for desktop applications, but also for any embedded software or more generally, everywhere there is a programmable chip.
The algorithm part is the most obvious for developers. It represents the processing of data and more recently the integration of libraries at different levels to provide compatibility between the various operating systems, languages, and protocols (read for instance: the web is a mess). Algorithms are the engine of the software. When developing resources are low the temptation is high to focus only on this part, because it produces the main output.
User interface is the steering wheel and the dashboard of the software. It becomes more an more an issue especially for portable devices, like a mobile phone or PDA where it really makes the difference between a useful gadget and a piece of crap. A bad user interface cancels all efforts provided by the software and hardware behind. UI is not trivial. The communications between machine and human goes mainly through a screen in one direction, keyboard, buttons, and mouse in the other direction. This is not always intuitive, and that's why UI is critical as machines become more complex.
Unlike Algorithm which is an hard science backed up by the power of mathematics, UI is an cognitive science. There is no formula for UI, only general guidelines for developers and eventually statistical studies bring the most reliable metrics.
Bugs are the dark side of the software. Nobody wants them, they are here. They are just part of the process. In our car metaphor, the bugs are all what don't work as expected from the annoying inside light that don't work when the door is open, to what can cause or aggravate an accident.
UI is a cognitive science, bugs are no science at all... They are unpredictable, and apart research projects around formal provers that are applicable in specific conditions, only intensive test suites can find out the bugs in the general case. But it remains the environment around bug fixing. I mean if we accept software have bugs (and we should do), then let's spare resources and prepare tools to handle them efficiently once they are found.
To take care of bugs, a dedicated team named QA is needed. If QA has a price, the lack of QA has a much higher cost. For most secure applications like embedded software in planes, QA can represent up to 70% of the product price...
The common point between Algorithms, UI, and Bugs is that they are much more easier to handle when they are taken account early in a product life cycle. It's not once the product is out that you start taking care of UI or tests ...or the algorithms!
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