I find krunner rather uneasy to use when it comes down to auto-completion.
Imagine, for example, that I have already typed the following two commands in
krunner:

vlc
vlc dvd://

Now, I would expect (as it was the case with KDE 3.5) that when I would start
typing "v" to get a drop-down list with the options "vlc" and "vlc dvd://" to
choose from using a shortcut key (tab would be ideal but it is now being used
to change between widgets).

In practice, however, if I want to run again the command "vlc dvd://", what I
get is "v[lc]" from which I have to press the End button once to get "vlc",
then press Space to get "vlc [dvd://]", press End again and then Enter.

As you can see, the process is much more of a hassle than it used to be in KDE
3.5; this becomes even more involved when having to run longer commands such as

firefox
firefox -ProfileManager ex1
firefox -ProfileManager ex2

where you need to press End and Space for every extra argument.

Is there something that can be done to improve this? Or I am just missing
something in krunner's functionality?

So, it seems that I was missing something. Pressing Alt-F2, right-clicking on the search-field and selecting Text Completion and Dropdown list, I managed to get the desired behaviour!