A colleague pointed me to the following article: Description of the Windows SharePoint Services 3.0 Cumulative Update Server Hotfix Package (Sts.msp): June 30, 2009. In it, it makes reference to the DISP_E_EXCEPTION error. Specifically, it states:
SPList.GetItems(SPQuery) fails when the item count reaches the threshold value 2000, and you will receive the following error message:
Exception occurred. (Exception from HRESULT: 0x80020009 (DISP_E_EXCEPTION))
Presumably, if you have a custom query on a list, and that query returns more than 2000 items (which is the case on the pages where I'm encountering this error), you'll get this exception. The fix for this, supposedly, is in the June 30, 2009 hotfix package.
I'm in the process of requesting that this hotfix be applied to our SharePoint server. I'll post again once that happens and let you all know whether it fixes this problem as advertised.
While searching for possible causes for this exception, the blog posts I found mentioned improperly-configured load balancers and other maladies, but not this 2000-item limitation nor the hotfix. Hopefully this post will help someone else out there who is having a similar problem on their system. Please comment if that person is you!