How do I rearrange the order of photos in an album in iPhoto?

Events and albums are different things (as are smart albums)

The direction you ask for are

View menu ==> sort - select teh sort you want

Or manually drag them into the order you want in the album

Within an event or a smart album you can not sort manually, you can sort ascending or descending by date, by title, by keyword or by rating using the view menu ==> sort

If you wnat to manually sort then you have to put the photos in a album

LN

View menu ==> sort - select teh sort you want

Or manually drag them into the order you want in the album

LN

What version of iPhoto and the OS?

Are you sure this isn't an Event?