I read how there is evidence that Neanderthals used to sail on the Mediterranean using primitive 'boats'. Have we discovered any of these boats, and if we have, what is the oldest of these Neanderthal rafts that we have discovered? My source says we haven't found any rafts and that most would have decayed since they would have been wood, however, that source was from 2012. Has anything been discovered changed since then?
There is not really a reason to doubt that Neandertals were capable of short travels over water, though clear evidence in form of a datable stratigraphy and correlation with contemporary sea water table is still lacking. Insofar, saying that they did sail the open waters is still a bit premature. No remains of a boat, raft or floating device from Neandertal times have been found until today.
It fits into the ever improving picture we get from our relatives in the human lineage. Work was also published showing that Neandertals were capable of symbolic behaviour (burials, personal adornment, painted objects) since the Eemian. (paywalled: https://www.nature.com/articles/s41559-018-0598-z)
That they made composite tools at the time and maybe earlier is known since long, for example from find sites Königsaue (reproted in the early 1970s), Campitello, Inden-Altdorf, and experimental archaeology:
and just recently arrived, evidence of cord fabrication from plant fibre:
Several paleolithic find sites exist with wood preservation (for example Aranbaltza, Clacton-on-Sea, Poggetti Vecchi, Abric Romani), even one from Homo erectus times (Schöningen). Technology and knowledge would have been there in the times of oxygen isotope stage 4 and the first half of 3 (80,000-40,000BP), but in a given case of a find site on an island one would have to correlate sea level stand and bathymetry, which is not a big problem these days, provided an exact age dating is possible.