I start to get really annoyed with the fact that the system adds code <br> to all of the Description fields if they are empty.
Is there any easy way to change in the files to prevent this action to happen?

You probably already figured this out, but you can of course switch to the html code view and delete the <br>, then switch back to html.
 
It shouldn't be very hard to change the php code that puts it in. Good luck figuring this out.

Yep, I have figured that out, but the next time I open the product again and change something, the <br> code is right back again. And if you are perticularly nit-picking (as my customer is), then you don´t want the description tab to show if there is nothing in the Long Description and so on..
And another annoying thing is that every other time, the <br> cannot be deleted, then you have to save and try again. Double the work in other words.