The sticky at the top of the forum is woefully inadequate for fixing the various issues with this game. I'm afraid that I am also no expert. So after those provisos, here's what I did:
1) Went to .../Origin Games/Mass Effect/Binaries.
2) Opened MassEffectConfig.exe
3) This verified that yes, in fact, the trilogy edition does come pre-patched to version 1.02. The information in the sticky and from several other snippy posters was incorrect regarding this. Check on the "Game" section of the config tool. If it doesn't read 1.02, then follow the instructions in the sticky. If it does read 1.02, you don't have to update. I didn't have to.
4) Close that tool.
5) Right click the MassEffect.exe.
6) Choose properties.
7) Switch to the "Compatability" tab.
8) Check the "Run this program in compatibility mode for:" box.
9) Select "Windows XP (Service Pack 3)" in the drop down.
10) Apply, click OK, etc...
11) Close Origin.
12) Remove Origin from the system tray on the taskbar. There should be an up arrow at the bottom right of your screen, close to the system clock, on the task bar. Click the arrow, then right click the origin symbol and close it.
13) Right click MassEffect.exe.
14) Click "Run as Administrator".
That did it for me. Hopefully it works for you.
---------------------------------------------------------------