Saw a couple of other threads that discuss something like this, but they seemed a bit different. Also saw two bugs (33552, 34770), but again they were not quite right, so thought I would post here and see if the zimbra gods wanted to either move the post or add to one of the existing bug reports.
Release 5.0.18_GA_3011.RHEL5_20090707151729 FC6 NETWORK edition
Using the Advanced client the Accept Decline buttons will only show up when using the reading pane. If the user view is set to not show the reading pane, the Accept/Decline buttons do not show in the window that is opened. This occurs with IE, Chrome and Firefox.
Using the Standard version resolves this. This occurs for 100% of our users.