Rafi, over in Life in Israel has a fascinating video which traces alleged Jewish ancestry in today's Palestinian populuation.
It's an interesting thought and something that I'd never come across before. My understanding was that the vast majority of "Palestinians" migrated to Israel over the past 150 years from Syria or other neighbouring countries.
The video claims that there is a high percentage of local Palestinians who actually have Jewish traditions and practices and may in fact be Jewish, having converted to Islam in the past 200 years.
There are many problems with the video - for example, they show Palestinians doing things like laying Tfilin, Praying from a Sefer Thilim, or having a Mezuza secretly in their homes, however the artefacts shown are clearly not handed down from previous generations (as the video implies), as it is new-looking tfilin, and the Tehilim is a Tanya-Tehilim handed out by Chabad at bus stations.
A more logical explanation (if the whole story is not fabricated) is that these Palestinians have adopted Jewish customs recently for superstitious reasons. I've often seen Arabs do things like Kiss mezuzot or act respectfully around Jewish ritual as a type of "good luck charm".
Other "proofs" of Jewish ancestry see less convincing, they found a Beduin tribe where they circumcise the boys on the 7th day and light candles at grave sites, both of which are similar to Jewish practices. But if that is all that remains of their Jewish practices, it is a big leap to conclude that these people are really Jewish.
The most compelling argument was common DNA between Ashkenazi Jews and local Palestinians, however there wasn't enough background to know how compelling this argument is - for example, do other Arabs share the same DNA, what are the odds that this DNA stems back to a few Jews who came generations earlier and married into the local Arab population.
Overall I found the documentary very interesting, I am yet to be convinced that the local Arabs are really descendants of Bar Kochba, however it is certainly food-for-thought.