Looks fine to me. What are you viewing it with?
It looks like you have two types of Minion Pro. In Acrobat if you go to File>Properties>Fonts you'll see a MinionPro-Regular Type 1 (CID). Can you select the paragraphs showing the problem in your .indd file and see what font is applied. Maybe you can do a Find Font and replace all with the Adobe Minion Pro.
I suspect the second subset is ligatures, or something similar, and not the issue. With nothing to compare to, it's pretty hard to know, but you definitely DON'T have any bold text, so what you are seeing is some sort of screen anomaly (and they tend ot show up in low-res printing, too), and th e most common cause for this is transparency of some sort on the page, but that usually shows up in ID as well.
I solved the problem, though it should never have been one (Adobe!).
I had a single line of text on my title page that was in Minion Pro Medium, while the body text on all the other pages was Minion Pro Regular (and Italic, and so on). For some reason, that single line of Minion Pro Medium was messing up the PDF. I have no idea why -- obviously some bug whereby similarly named fonts get randomly mixed up.
BTW, I checked the PDF I uploaded for your viewing, and in it the whole font is incorrect: it is now all thickened rather than regular. When the same file (pre-upload) is viewed on my computer in Adobe Acrobat Pro 10.1.15, the different font weights are apparent, so there is something, too, about which PDF application it is viewed in. I also tried printing the doc from the online viewer, and it definitely prints differently than directly from my computer.
Once I removed that single line of Minion Pro Medium, the file exported properly. I can replicate the original problem by changing that single line back to Medium.
Thanks for all your suggestions.
Well, the plot thickens. I thought the problem was solved because the PDF looks normal now, but when I print a page on my Lexmark, the thickened font returns. No idea. Also have no idea how my commercial printer will print this file until I order a proof. :-( This is so not good.
I also cannot get InDesign to print properly from itself: if I send the page to the printer, all that prints is the master items (the header and footer); everything else is blank. So maybe this is not a font problem but a printer problem in InDesign, whether to PDF or to a physical printer?
BTW, tried to change this thread back to unanswered, but apparently no can do.
ID is not know for it's native printing capabilities, and in this case I would definitely recommend you export to PDF using the same settings you will use for the one you send to the printer, then print that from Acrobat.