There should be an un-Thanks button for that post Ucof!
Seriously, you CAN'T clean the headlining, it's made of seemingly recycled paper compressed and printed with a dot pattern. It really does fall apart. It's the absolute lowest grade of material possible; an area where FIAT really cut costs (except for the headlining of the Mk1 Uno Turbo, which is a totally bespoke and irreplaceable material).
I have also applied various types of thick paint to Uno headlining, which is reasonably successful but can stink
Thin paint just soaks in invisibly.
Best bet is to go to an auto trimmer and buy some REAL headlining material, as used in normal cars (not the Uno...) Headlining cloth has a thin foam backing and comes in a hundred shades of grey (well, not literally, but it varies from a warm grey (which you want for the Uno) through to a cool grey/blue. It comes on a wide roll, plenty wide enough for the Uno, and a tape measure will tell you how long it needs to be - allow a bit extra for the ridges around the sunvisors.
You'll also need a spraycan, possibly two, of contact adhesive - buy the best type you can find, ideally one large can of 3M Headliner adhesive will do the job. You're looking at about NZ$90 (35 pounds) worth of materials.
Remove the headlining from the car - easy on the Uno, it comes out through the tailgate opening - remove the interior light mounting (noting which way around it goes), then spray the whole area with a good even coat of adhesive.
Spray the material second (it dries fast) - then carefully roll it into place from the back to the front, being very careful to start off straight
, avoiding and smoothing out wrinkles as you go. You'll find the material really stretchy so it copes with the hump in the middle very well, and the tricky bits around the visors (keep it fairly taught).
Once it's all in place, trim the edges exactly (fold over and glue the edges if you like, you can always trim them off later if the headlining won't fit properly), cut out the holes for handles, interior light, mirror etc. with a sharp knife. Refit to the car, using the interior light housing to hold it up (it has a twist-lock fastener).
There may be the odd small flaw in the result - particularly if there are big gouges or flakey areas in the backing - but generally-speaking, it will be a huge improvement in every way except originality.
I've re-trimmed headlining on a FIAT Croma ('88 model), Tipo (just as bad as the Uno), BMW 320 ('93 model, fell down like a tent), and my Uno Turbo, though in the last case I used black speaker box carpet for that warm fuzzy feeling.
The following applies to the Mk1 Uno Turbo and other cars... where removing existing foam-backed material, the foam will have disintegrated and must be scrubbed off the backing completely. Don't bother trying to re-stick existing material - that doesn't work, the disintegrating foam undermines the adhesive and without a foam backing, the material is never smooth.
-Alex