… subject of desktop Linux, I will mention the following things I feel are required to improve the end-user experience. [This only details things I believ are important to the _end-user_ – there are different things I think are important to developers]
- Improve mime-type handling. In Windows, everyone is used to simply double-clicking a specified file and having the correct application open it. This is available in Linux DEs as well. However, there are a few issues. First, both KDE/GNOME handle mime-types differently (to the extent of having different preferred applications). This is confusing for the end-user. Thankfully, a freedesktop specification has been created to deal with this (as far as I know). In GNOME, the dialog to change mime-type handlers is ugly and over complicated. I doubt any reasonable user would be able to change the default handler.
- Improve the GUI interactivity of X. This is more complicated and depends on a number of factors, including your window manager, toolkit, video card and driver quailty. However, I can say the following. At least on my machines, X performs slowly in relation to the Windows GDI (ATI card). This is partially explained by the fact that the Linux ATI drivers are not as polished as the Windows ones…but it is not the only cause of the problem. People interact with the GUI all day. Having X look (or even feel) slow is a big problem. 
- Decrease the complexity of installing 3rd party drivers. I have always done my research in choosing my hardware and have generally chosen components that are well supported across the board. As a result, I have had very little problems. I should also commend the kernel hackers greatly in the skill they have demonstrated in supplying a vast range of excellent drivers for a variety of hardware. However, in my opinion, it can be very hard to supply a 3rd party binary driver and have the user install it quickly. Case in point – the linux-ntfs project supplies a range of rpms for a variety of 2.4.x series kernels. Why is it not possible to supply a single 2.4.x driver that will work for the entire series (I intend to find out). Some drivers require users to compile… If Windows, can allow 3rd party drivers to install with a few mouse clicks, the question must be asked – why can’t Linux be like this?
- Improve/include greater plugin support for media formats and ensure that websites using these formats are accessible out of the box…
I’m sure there are more. Comments are appreciated and I will add more as I remember.