Ok, I continued to read some more, and everything worked fine in the beginning (it seems it always works fine first, and then it starts to not work, and get more and more errournous...).
After a while this happened:
As you can see the underline does not go all the way (is this because it goes over separate spans?).
Hightlight didn't stick.
Choosing a part of the text, the hightlight worked.
Trying to add the second part, made this:
No matter what I did, I could not get all the text to work.
I tried to do one word at a time.
That seemed to work.
On the next page, it worked to mark everything.
On the page after that, which looks the same, I couldn't get the whole page.
After that I gave up and continued reading in the epub-version of the same book (which I simple file copied on the device). Worked fine with highlights for the time I read.
Any more thoughts?