You can try doing whatever you want with the window(in a window mode, of course), but with full-screen it's not like that. After few alt+tabs, or a screen move(alt+drag) the game will no longer be at full screen - you'll be able to see the task bars, or even worse, the "window" will be lost, but the process will be on.

If you play full-screen, do not try moving the screen.

Also, when doing alt+tab on windowed mode, when you get back, the game will be freezed. Just press alt+enter, and it will get back as normal.

While playing the intro, if you click your mouse without previously being moved, you will open the trash.

 Move the mouse when the "blizzard" intro comes in, and click. This happens because the mouse possition is at the bottom-right corner of the screen.

Window managers often have the alt key bound to certain features, especially the alt-click. This is not a wine bug. If you have problems with the alt key in any way do not report it. Fix your window manager. I'm not going to list steps for every one because there are too many possibilites. Figure out yourself or ask in a help forum (here is okay... but be warned all I use is TWM). If you are desperate, turn off window manager managed windows in winecfg.

KDE

Go into KDE Control Center, expand Desktop, click window behavior, then click window actions tab. You can turn off the alt-combos. If you want to make window specific settings, click on window specific settings under window behavior on the side.

GNOME 2

The option to change the key binding is in System Menu -> Preferences Menu -> Windows.