That slot looks to be asymmetrical for proper operation. Check it a few times to make sure it works before setting the rivet.
That's entirely possible. But I doubt it. There was obvious wear. How much the obvious wear elongated the rivit shaft and latch plate slit could be up for debate. This does bring up a concern that I may have not documented.
There is a guide for the rod that goes to the remote handle, it's stamped straight in the latch backing plate. And the latch itself should, as far as my limited mechanical knowledge permits me, should only have lateral movement.
The rod connecting the latch to the remote handle has bends, which should eliminate the need of excessive slop at the rivit. Again, this is my first time on these old cars, but I wouldn't do all this if I didn't spend some time inspecting to determine some mass of metal was worn out and missing.
If you like, I can grab more pictures during the next sides repair. I could go into overlaying my theory over a pic of the latch with mspaint.
Then again you may be correct. But my two sides weren't equally worn, driver side was more wobbly, which kinda confirms my theory as it'd be more used. But doesn't discount yours.
The issue of worn parts is on the floating latch, it is not part of the remote handle shaft. If anything needs slack it would be the remote handle shaft. You'd expect the actual latch to operate perpendicular to the door jam.