When you attach the door mirrors, do they simply screw into the panel, or are there supposed to be little nuts or inserts on the inside?

I have seen them with both self tappers and nuts/bolts. If they are original mirrors up near 1/4 window then would most definitely be self tappers.

What model?

Its a 120y and yes the mirrors appear to be fastened with self tappers - just wondering if that's all that supposed to be there as when I carefully reattached the mirror, it seem to come loose very quickly.

Maybe I was just a bit too careful not to over-torque it.

Maybe try some nuts and bolts, you just can't get your fingers up the top of the door thats what I have found, never owned a why so can't help much more.

The originals were fitted with self tappers, but I used stainless bolts with a nylock nut. Stronger than screws as they dont bite into very thin metal all that well. You can get your hand un inside the door ... just

Just use 100 mile an hour tape

Once the holes oval out a little a self tapper will work loose very quickly.
I ended up using some 4mm diam. aluminium pop rivets to fix my door mirrors on my ute.
Makes them harder to remove, especially if you are trying to pinch them
Don't need to remove any door trims and they look neat enough

I'm not the biggest fan of the stock mirror spot on the Y's and the supercheap aero-look mirrors on my orange sedan have been on there way longer then I've owned the car for and never come loose. I like the sound of the locknut idea though if I change them to something awsomer