|Picture from the BBC report|
Scott Bashoor has pointed out to me that the BBC has published a report about the redating of a Torah scroll at the University of Bologna in Italy to around 850 or more years old. It was dated to the 17th century by university librarian Leonello Modona in 1889, but was recently redated by the university's Professor of Hebrew Mauro Perani. The redating is reported to have been made on the basis of carbon dating, an oriental Babylonian script, and lack of conformity to Maimonides' rules from the 12th century.
The report quotes Mauro Perani as saying that this would be "the oldest complete text of the Torah known to exist," but surely this is incorrect without some qualification. The Leningrad Codex, for instance, is complete for the Pentateuch and dates to A.D. 1008/9. I'm not sure off the top of my head how old the oldest complete Torah scroll is, however.