I know you already have your solution, but two more comments:

> Often text lines go beyond the page limit of the A4 format at the right side. So the text is there but not visible.

(Kind of off topic here :)

I'm not sure if you're talking about print or online viewing, but this sounds like the document was produced for another paper size like letter ¹.

So rescaling "to fit" or changing the page format on the creator level should help here.

Maybe try this inside your "Pro Acrobat" tool ? ²

> Or much better could I automatically minimize the right border of all text boxes to be in the visible are plus a small margin?

Hmm this depends on the level of semantic info available. Many tools only have positional informations and lack your/ artificial "intelligence" to tell what should be resized and what not.

For instance you don't want your page numbers and headings to skip because the main body is reflown.

Even with an elaborate CPAN module you'd need a lot of try and error.

Updates

¹) PS: metric rules! =D

²) there are plenty of online services offering to resize PDF