You won't know until you shoot a roll of film in it, but I am 99% sure that the leak is at the hinge area on the back door. When you open the camera's back, you will see that there is supposed to be a felt strip on the camera where the door shuts and covers that hinge area. It's surely deteriorated away.
I would just put film in it, and take some electrical tape and tape up that area w/ a strip of tape on the OUTSIDE over the hinge. Might as well do the same on the other side where it snaps shut. It's possible that the top and bottom of the door areas may have a light leak too, but I doubt it. Just do that and run a roll through the camera and see what you have, and also see if you like the camera. They're fun little cameras, and very simple to shoot.
If you like it, there's lots of articles on the web that show how to put your own seals in the camera w/ just a bit of black yarn (unravel it and use just one of the threads, not the whole thing) and some glue. Usually, if you just do that and use a very small screwdriver or a dull knife to stuff the yarn it it will stay and you won't need to use any glue. Don't clean out the old stuff (which is gonna be almost gone anyway), just put in the yarn thread and use the old stuff that's in there to hold it in. Close the camera's back overnight and you're set. The door hinge area can be addressed w/ a very thin piece of cloth or felt glued down inside the camera at the appropriate place. It sounds like a PITA, but it's simple to do all this.
Here's a link to the manual if you don't have one. It's nice to give Butkus a donation of $3 for his time and trouble scanning these things and offering them to people. Just click on the blue writing that says "Click Here To Continue To PDF Booklet". Happy shooting!
http://www.butkus.org/chinon/nikon/nikon_em/nikon_em.htm