As of September Chrome will not do java.
How this affects Blackboard is that Quicktime, Windows Media, and Flash files won't be visible within the Content editor
Also, collaboration needs to be done in Firefox (or IE theoretically)
And, although it's rarely used, uploading files directly will only be possible in Firefox (or IE theoretically)
Finally, in the remote chance that you are using pre-2010 SCORM files, or math equations taken from Web-CT or Angel, they will also only work in Fierfox and IE.