Use a putty knife to release the clips that hold the top down.

(slide the putty knife, from the front of the machine, in between the top and the cabinet 1 to 2 inches (??) from the left & right edge.   Press straight in to release (1 clip each side)).  

Be careful of the "filter flo flume" in the seal opening as you lift the top up, you don't want to break it

Once open you'll be able to see all the hoses inside, along with the fill flume.   You can operate the machine with the top up to check where the leaks might be coming from.

You will also be able to check the outer tub, under / around the tub seal for rust.   This is a common problem and I'm guessing this may be part of the problem.

Also, do not fill the tub full with the top up, OR if you do, be VERY careful when you put it into spin as the water WILL spill over the top of the outer tub.

I hope this helps!

Kevin

As RevvinKevin said, caution with that fill flume as you lift the top. Once you get the hang of removing it from the flexible plastic/rubber guard, no problem.

The fill leak------check in rear left corner, from where hoses screw on to the back of the machine, all the way to where it shoots into the tub. Any/all of these parts are replaceable, there should be a short hose from the valve to the side of the tub, then a vacuum break plastic assembly, then the final nozzle into the tub.

Spin leak----during the last half of spin, it spray rinses, so maybe you are leaking each and every time it fills. 

OR---the top of the entire machine is also the top of the outer tub. During the first part of spin, with even just a half load of water, the water runs high enough up the sides to go over the edge of the tub. There's a rubber seal all the way around the tub top, should be tightly pressed against the machine's top underside. Check all around that, see especially if you can find water drops running down the outside of the tub. When fully loaded, spin creates a hell of a lot of water right up against the lid, by design. Whenever I am all the way done working on a Filter-Flo, no more opening the top for months, I use Vaseline around that rubber gasket. With all the ridges it has, I figure the Vaseline won't all wear away quick, can help that last ridge or two against the few drops that make it that far. But that is after making sure that it seals well around the flume, against the clean dry lid, etc, no cuts or breaks.

A fill leak or spin leak should be easy to find, diagnose, repair. GE's are good machines. It always helps to watch in use, see exactly where/when the water comes from.

I opened up my 1979 last night for a quick peek. In addition to the hoses and vacuum break and nozzle for the incoming water, there's other places that can leak.

Mine has an overflow tube, stuck thru nearly the top edge of the sides of the outer tub. Also a bleach dispenser tube, left front area, near the top of the tub. And the filter nozzlet/flume, roughly 1 o'clock position.

But if it leaks during fill, your first bet is checking the entire rear left area: double solenoid valve, hose to plastic vacuum break assembly, hose and nozzle entering tub..

Keep us posted----it's a good machine and sounds like simple repairs, inexpensive.