A constraint of Mozilla is that it doesn't have extensive centralised management yet. You have IMAP, LDAP, NLTM and security support, but not yet extensive centralisation of user profiles. You can use a file server without any problem, but you need to check that your current arrangements naturally apply to Mozilla. If you're deep in the mindset of Microsoft Desktop Applications, then some of Mozilla's more obscure features may seem foreign at first.
On the plus side, there have been very few critical patches issued in Mozilla's history since 1.0 was released. You can pretty much forget about monitoring the news for Internet security flaws.
Another issue is any Website content you might maintain. If it's been created with Internet Explorer specifically in mind, then, not to put too fine a point on it, it may be awful. Such IE specific pages need to be reviewed to see if they need a little standards-oriented tidying up. The worst of them won't display at all in non-IE browsers. HTML 4.01 is the most conservative standard to aim for, and the least work. XHTML 1.0 is a nice future-proofing strategy that compliments migration to standards-compliant browsers like Mozilla (or, in fact, anything other than IE). Fortunately, both IE and Mozilla have "best guess" features that kick in for really poorly created pages. You can live with that if you don't yet want to migrate to Web standards. Such migration is inevitable, though.
Most of the above points, however, are technical. It's well established that the main cost of migration is re-training users. That's your number one issue. Perhaps soon there'll be a Mozilla version with exactly the same point-n-click workflows as Internet Explorer, but that will only happen if people like you recognise how important it is and hassle the Mozilla folk about it. Fortunately, existing browsers have quite a lot of overlap to start with. A toolbar button's much the same everywhere.
This was first published in April 2004