I notice that when footage is shot with the rear eyepiece, a lot of things that may drop in on the edges of the lens, such as wires, filters that droop down slightly, etc, all do not appear in the rear eye piece, but when thrown up on a monitor, show up quite a bit.

I have shot footage merrily recording away thinking all looks well, only to throw up the footage on a computer monitor and a dang filter holding arm drooped down and shows up the sides of the frame, thus ruining the footage.

Is there a way to get the eyepiece viewfinder to approximate what shows on a computer screen?

Depends upon what cam you have.

FX1, no.
Z1, yes. ALLSCAN mode, p.87.

Such unacceptable overscanning is a relic from the days when feeble power supplies were fitted to CRTs. The Z1 option / method of showing the full frame was to reduce the image to a silly little rectangle within the screen area - to 'warn' you that you were viewing what the tape was recording.

Thankfully that's all over, and the NX5 shows the full frame in v'finder and on top screen.

tom.

Is there a way to get the eyepiece viewfinder to approximate what shows on a computer screen?

To expand on what Tom said, go into the menu, scroll to "Others", choose "Assign BTN" and assign "Allscan Mode" to one of your camera buttons. Then when you press that button, the image will seem to shrink, but it's actually showing the complete frame.