I am in the process of buying a 1976 house that has no GFCI. Is there a spec on where in the leg the GFCI outlet needs to go? First outlet, last outlet, or doesn't matter? I would assume it really doesn't matter since if it trips it will open the circuit.
If wired correctly, the outlet will protect all the outlets "downstream". So, it is recommended to put it at the outlet closest to the service panel, to protect as many other outlets on the branch as possible.
That said, it's not against any code to put it elsewhere; it just won't protect the other outlets on one side. After installation, press the "Test" button, and make sure that the other outlets on the branch are also disabled. If there are any that remain live, then they don't earn the blue sticker.
Make sure you put the correct wires in the correct places. Connect the "line" wires first, and test the outlet by itself to make sure it has power. Only then remove the yellow tape and connect the rest.