I have seen a few varieties of character-drop like this one, but never the same thing twice. Is it possible that...
1) you have Missing Glyph Highlighting turned off? Because if you typeset with no Arabic-supporting font applied to your text, and you have the pink highlighting turned off (and Missing Glyph Protection turned off) then when you export it will behave in this way.
2) you are actually printing to Postscript and distilling? I know, probably not! But if you are try exporting something like PDF X/4.
3) You are using a combination of Smallest FIle Size and not embedding the font? Try playing with the font subsetting percentage to be found on the Advanced section of PDF export options window. If you set it to 1%, it means that the entire font will be embedded, which is useful for some Arabic fonts whose designers put the ligatures in, ah, unexpected places.
If you are free to post the PDF and INDD somewhere (like on Dropbox?) I'd be happy to take a look to see if I can reproduce your error, and perhaps suggest a fix.
Thanks for your answer. I tried everything you suggested (though my InDesign's preferences are missing the option "Missing Glyphs Protection", see below, but I managed to track them through the preflight panel and a script I downloaded from Peter Kahrel's site: http://goo.gl/oP53WU and there's no missing glyph in the document – I use Myriad Arabic for the Arabic text.) but nothing works.
I'll send you a private message with a link to the files, because I'm really lost here.
Many thanks for your effort you put in this!
I checked out the file, and there's a character style (leftover from the source English file, obviously) that has Small Caps applied to the text. Why this should alter the text at all is a mystery to me - yet another reason for me to wonder about who at Adobe is in charge of internationalization issues.
If you remove the Small Caps attribute (and perhaps the All Caps attribute as well - I didn't dig that far but I assume that it would be a problem as well) then the Arabic text exports correctly.