I just recently purchased a Dell computer and have been getting this error message from day 1 when I shut down.

Explorer.exe - application error the instruction at "0x00109e60" referenced memeory at "0x00109e60". The memory could not be written.

The message indicates that it will run a debug if I hit 'OK" but it does not appear that it really tries to debug the error.

Every thing else seems to run OK.

Anyone have any thoughts?

There's nothing of consequence on that specific err. on the web. Appears to be an attempt to write to (modify) paging file. If you haven't already done so update the OS, it's worth a try. Failing that, call Dell's tech support, a machine no older than that shouldn't be giving that type of err. this soon. If they don't want to help, invite them to take it back.
Debugging requires some inbox OS app. that isn't normally loaded at setup.