I suspect it might be one of the unofficial themes, because I had a similar problem previously with my (Series 40) 6270. I applied an original theme, powered off and on again, and no problems since then. I also removed the unofficial theme from my handset.
Of course it could be a virus or other nasty and, yes, you should have an anti-virus program on a Series 60 phone. I use F-Secure, and it works well.
.