OpenOffice has said only one actual bug was discovered, and that flaw has been fixed already. But the research, by the French Ministry of Defense, also points out that many security flaws have already been discovered in Microsoft Office applications, claiming that these are "easily transportable to OpenOffice."
Of course. OO.org contests that as a whole, OpenOffice is inherently more secure than MS Office. Due to the integrated nature of MS Office, this is probably true, but OO is still a huge suite that likely has many flaws. The report that started this controversy identified six, though we'll probably have to wait for the OO team to confirm them before we can assume the report is accurate.