It takes time to download the new fixes to each desktop.

Rarely will you need to get updates that often. The vendors are already very quick to get fixes out to everyone when a new virus appears. So daily updates will matter only if you are the unfortunate one to get hit first.

We are considering doing virus scanning on all incoming e-mail.

It is expensive, it creates a bottleneck at the mail server, and it isn't clear that such a scan will be all that effective.