Version:           1.10.3 (using KDE 4.1.3)
OS:                Linux
Installed from:    SuSE RPMs

You open a new mail and you get the automatic address search and completion into action (which is a problem in the latest KDE packages; see Bug 176787). 
If you then have several adresses fitting the typed letter combination in the "To"-field 
 a combobox opens from which you can choose among several recipient addresses. 

There are two bugs associated with that: 
1) You cannot access the combobox via any standard keyboard action. The input focus is not automatically switched to the combobox. You cannot move up and down to choose the right address and use the Enter key to complete your choice and get the address into the "To" input field. 
2) If you use the mouse to choose one address entry the address data will be filled in in the "To" input field. However, the Combobox will not close ! It remains on the desktop as a separate window and hinderness for further interaction with the email composer. You have to move the composer window and then click into another address filed (e.g. CC) to get rid of the Combobox.   

So in my opinion the programmed interaction between 
a) the window for composing the new email and 
b) the combobox of the automatic address search associated with the address fields of the mail is really buggy in the present KDE 4.1.3 releases. 

My present package is form a SuSE repository. Infos from the Help menu: 
KMail Version 1.10.3
Unter KDE 4.1.3 (KDE 4.1.3) "release 63.3"

I am quite sure that I did not have such problems with 4.1.2 releases. 
 
In case this is of interest: I use the latest x86_64 nvidia driver for 7800 GTX card. Compiz is running on my system, but the bug seems to be independent of the window manager.