Recently, has come under some scrutiny as people express some security concerns over the office suite. While a single flaw that was a major point in the discussions has already been patched, another complaint concerning the suite is that many flaws found in other Office suites (namely MS Office) are "easily transportable" to OpenOffice:

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. 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.