Thank you so much for your answer.
The url is http://roverground.cz/2014/03/10/svedectvi-o-syrskych-uprchlicich-v-turecku-2/ for example.
I've investigated some more and found out, that Bootstrap is probably in some sort of "argument" with Jetpack Carousel (based on some other user forum question about other, similar plugin).
After some investigation, I have found that somehow output code includes stuff like:
<div class="jp-carousel-slide" style="left: 0px; background-size: 100%; width: 1024px; height: 674px; top: 2081px; position: fixed; -webkit-transform: translate3d(-942px, 0px, 0px); background-position: 50% 50%;"><img src="http://roverground.cz/wp-content/uploads/2014/03/Untitled-Scanned-82-e1394504227492.jpg" style="width: 100%; height: 100%;"></div>
As you may notice, the "top: 2081px" might be source of the problem.
This problem occurs on more occasions, like
<div class="jp-carousel-info" style="top: 4821px; left: 110px; right: 110px;">
So far I edited plugin css file, hardsetting top values as !important but that is no long term solution.
Thank you in advance for any help, I am struggling with this for days now and it seems to be way beyond my skills :)