Hellcat: the first big difference is that the Uno has only one wiper

So, there isn't any linkage.
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The Tipo is not really a big Uno - the basic construction is very different (e.g. lack of roof rails, clever door and bonnet hinges, bonnet shape, panel attachment, underbonnet structure (big gaps), seats and trim all secured differently, and absolutely no electrical bits in common!)
The Croma, on the other hand, is more like a big Uno. Compare, say, a Croma rear light with an Uno rear light, and a Tipo rear light. The Tipo is a much more modern, sealed design.
</rant>
This is only possibly of interest to someone who has worked on a number of different FIATs and studied their strengths and weaknesses!
Now meanwhile, does the Uno wiper spindle have slackness just in twisting, or up-and-down as well? If you can move the spindle up and down, you might have to consider enlarging the hole in the housing, and using a very thin piece of metal (such as a feeler gauge blade) to wrap around the shaft and eliminate the clearance.
But really, I believe this is a rare condition, even if you have found another like it! There is always a certain amount of movement at the wiper blade. I just went out to my garage and measured 6cm free play at the end of the blade. But I could not detect any up-down movement in the spindle - only the twisting.
If you open up a wiper motor, you'll see that there are gears inside to modulate the speed of the wiper. There is a crank, but also these gears to sweep the wiper faster in the middle of the travel than at the ends. The gears live in a big splodge of grease and you will not detect any wear. So, the slackness comes down to it being made in Italy, where no-one cares about such details. If you would like the wipers to be smooth and precise, you'll have to buy a Japanese car.
-Alex