Make It Look Like a Book in the Acrobat PDF
With book documents, chapters usually start on a right page. If I want to make a pdf, the spread option does not work for the last page from one document and the first page from the next document. I get single pages for these two. (This is not for final print, but only to show clients what their pages look like.)
Making a PDF of a book actually look like a book isn't as straightforward as you might hope. It is tempting to turn on the Spreads checkbox (in the Export PDF dialog box) in order to show what the book will look like, but I encourage you not to. First of all, as you found out, InDesign cannot merge the two pages (last page of one chapter and the first page of the next) together into a single spread. But second, all you're really doing is telling InDesign to pretend that the whole spread is a single page -- and that the document is made up of single-sided pages. Of course, you'd also need to draw your own line in the document to show where the spine is... Blech.
Instead, give this job to Acrobat. After opening the PDF in Acrobat, you can adjust the view (View > Page Display) to show the spreads. Make sure the Show Cover Page During Two-Up is selected, too, or else page 1 will become the left-hand part of a two-page spread.
But you don't want to have to tell your client to do this. So open File > Properties (Command/Ctrl-D) and, in the Initial View tab, set the Page Layout to "Two-Up (Cover Page)."
Then click OK and save the document. That way, when you client opens it, it will open just the way you intended. (Unless they open it in some other PDF viewer, like OS X Preview, which doesn't read the Initial View tag properly. In that case, you're back to telling them to choose View > Page Display > Two-Up.