Interference with ideal beam I'm thinking about this setup and am a little confused:

An ideal beam (thin, no divergence) is entering from the left. It is split up by an ideal (50:50) beam splitter BS. They are united again at the screen S by an appropriately placed mirror M. The screen shall be completely absorbing. 
I think it should be possible adjust the dotted path in such a way that there is destructive interference with the dashed path at S. But where did all the energy go? Which of the above points is impossible to achieve?
 A: 
An ideal beam (thin, no divergence)  

from which one can say that inclined (to each other and to the screen) plane wavefronts of a finite width are incident on the screen.
At one point there is no net electric (and magnetic) field but what is happening around that point?
There is a net electric (and magnetic) field with energy carried by the fields being absorbed by the screen.
A: As the two beam interfering are not colinear, you will get vertical interference fringes. You can adjust the distance to have destructive interference for the central fringe. The energy will go on the constructive interference of the other fringes. 
So for me the unachievable in this experiment is to select only one fringe without using a vertical slit.
A: The fact that the beams interfere destructively at the screen does not mean that they will destroy each other everywhere else. 
After the beams interfere in the plane of the screen, they will be partially reflected and partially absorbed by the screen, i.e., their energy would not disappear.
In this sense, it is no different than the interference between any two properly polarized coherent independent beams, which could take place anywhere the beams overlap, but would not affect the beams once they have passed the overlapping area.
A: There are some neat things to consider in your experiment, but first of all, no energy is lost. A similar example is 2 tsunami's, one leaving Japan and the other leaving LA, and one being a depression/subduction and the other being the opposite.  The waves meet at Hawaii, they cancel, everyone is saved, but unfortunately after Hawaii the waves reemerge, one continuing on its way to Japan and the other to LA. This is conservation of energy.
With your experiment consider another example of a thin film reflection coating, say the coat is 500nm thick which will block all 1um (IR) light (provided it is coming straight on).  What happens to this light?, it gets reflected becoming a standing wave with the source.  I have assumed your ideal source is monochromatic.  I think your setup will effectively be similar, the energy building up in the source.
(Another detail to consider in your beamsplitter is that one of the waves reflecting of the front face or the one emerging actually gets a phase change in the process.) 
