Now, I am 100% sure it occurs when browsing through desktop when trying to load a movie or ROM. Sometimes it doesn't crash. I will try to find the real way to make it crash. Since it seems to happen only on desktop, I think you should try finding the solution.
edit: I don't know if it is useful but using windebugger gives me this:
(284.21cc): Access violation - code c0000005
eax=02032038 ebx=00000000 ecx=0672f1da edx=0672f1d2 esi=0672f3e0 edi=0029bf28
eip=7ca614ae esp=0672f134 ebp=0672f37c iopl=0 nv up ei pl zr na po nc
cs=001b ss=0023 ds=0023 es=0023 fs=003b gs=0000 efl=00000246
SHELL32!SHCreateQueryCancelAutoPlayMoniker+0xf7f8:
7ca614ae 8b08 mov ecx,[eax] ds:0023:02032038=????????
Edit: The easiest way to make the bug happen is by opening the ROM then play the game normally, sometimes use frame advance, pause, save and load state and do this for 2 minutes then browse for the ROM on desktop but don't open it immediately. Press the letter of any known files, ex. Arkanoid, you should press A, and also some other file that share the same first letter. Hold it then "left click" with your mouse on any file and FCEU should crash.
If it fails, redo those steps.
Another bug happens when trying to open a zip file that doesn't contain a valid ROM. You will get an error message. Now retry loading that zip file again or another one. OOPS, it crashed.