This should be fixed in latest MM 4.0.0.1382+ versions. See http://www.ventismedia.com/mantis/view.php?id=5442

This has been partially resolved in 1363.
The resize arrow no longer appears over the title bar on either screen.
However, the minimize, maximize and close buttons have no effect when clicking on them when MM is on the second monitor.

If it helps to debug, I've set my primary monitor to the right monitor, but dragged my start menu to the left monitor.
MM window buttons are not responsive when MM is on the left monitor. Everything works as expected on the right one.

Edit: possibly related? (as to why it's partially working now) http://www.ventismedia.com/mantis/view.php?id=7612

I have exactly the same issue with 1361. I repositioned MM4 on my second monitor, but the right edge of the window is off the screen and there's no way to grab it. Clicking on the titlebar next to the menus doesn't have any effect. The minimize/maximize/restore buttons are off the screen and there isn't any way to get the entire window back on the screen. Very frustrating.

Also, there is no system menu when I click the circled monkey at the top left (most programs show "move/restore" menus, but that may be by design. Nothing at all happens when I click that circled monkey.

The only way to close the program is to use Alt+F4 or the close item on the taskbar jump menu. And when I reopen, MM4 reopens half off the second monitor screen again.

Still occuring with 1361.
Win 7 x64

TO reproduce:
Start MM, maximize it on one screen using the maximize button in the top right.
Unmaximize it with the same button.
Drag the entire window to another screen.
Attempt to maximize it by clicking the same button.

Notice that the mouse has changed to a vertical resize arrow. Occasionally the File/Edit/View etc. menus dissapear as well.
Can only be fixed by a restart of MM it seems (you can still move and resize by right clicking the icon in the taskbar)

In addition to this, you can no longer click the title bar - it turns into a resize arrow ONLY - so it's impossible to move the window through the usual means.
This is using the default skin.

I assume they're related.

In Windows 7 x64, dragging from one full screen monitor to another, or sometimes when maximizing, those menu bar items are not redrawn. hovering over them redraws.