Just wondering if just simply swapping the original 72 pin connector, with the pin connector from the Game Genie would "fix" an NES so it would work all the time.

Yes, that would fix a NES so that it would always work. Unfortunately, it's not as simple as it would seem, as the connector designs are different. It's certainly possible, and has been done before. It would make a good first mod.

the only concern i have in attempting this myself is that using a different cartridge connector would require that i add or take out a component within the system. check out this video at around 22:25, and check out how he connects the new cartridge connector to the system. video: http://www.youtube.com/watch?v=YDGR2MiCyYs. If i were to open my nes, and simply solder the new cartridge connector from the game genie, would this work? or would there be any complications??? thanks again for any and all help!

Yeah you can jut solder it right to the nes board; that's what I did for a nes laptop I'm trying to build. The hardest part is making sure you wire it correctly. The way the original connector works makes it kind of confusing, at least to me, since the top connections of the slot are connected to the back of the board.

best thing to do is keep have a game inserted in the connector when you are soldering it in so you don't get confused.