I found that transitions worked sometimes or not at all on several other systems with different versions of Acrobat or Reader.
Between my experiments and advice from helpful users on The PDF List, a mailing list provided by PDFzone.com a pattern emerged. The results were nicely summarized on the list by Max Wyss of PRODOK Engineering who I'll quote here:
Transitions only work properly in single page mode. This kind of makes sense because there is only one transition which does work at a given time.
Up until Acrobat 5, transitions assigned directly to individual pages (for example via PDFMARK) worked in normal view as well as full screen view. Apparently, somebody at Adobe considered that to be a bug (transitions are presentation stuff and our customers want transitions for full screen view only). So, since Acrobat 6, transitions no longer work in normal view.
Transitions were simply not implemented under Mac OS X until Acrobat 6, and then only in full screen view as above. However, transitions work "normally" when running under OS 9 even in older versions of Acrobat.
So, we have the following conclusions:
In normal view, single page mode, transitions work under any version at 5.05 and older, whereas for Mac only under OS 9.
In full screen view, transitions work on any platform and under any version except 5.05 under OS X.