This is happening to me again right now. I have not been using remote desktop or any resource intensive applications. Just mIRC and Chrome really, although earlier I was plugging in my laptop to a dock for external monitor testing.
The min/max/close buttons are different styles as in the previous posts. When I switch to a different window, the duplicated icons on the left both update to show the appropriate server/channel/query icons. But only leftmost of those icons updates the menu when left clicking. Server menu is apparent because 'Certificate' is in the menu. 'Channel' is apparent because 'Nick List' is in the menu. The right duplicated icon is always showing the channel menu, even if I'm now looking at a server window. Selecting 'Nick List' at this point causes mIRC to beep. When on a channel window, it correctly sets that channel's nicklist state.