I've noticed that i still have to complete 4 regular missions out of the 26 in the campaign. However, i have no idea how to do it. When i press "Continue Campaign" there are no unplayed missions in the list. Also, i do not have any saves from previsou play, since i reinstalled my computer lately. Is there any way how to get to those unplayed missions without playing the whole campaign again?
Missions I missed:
Echoes of the future
Piercing the shroud
A sinister turn
In utter darkness
It sounds to me like you've missed the secret mission "Piercing the Shroud" and the alternative choices on the Tosh/Nova Selendis/Hanson and Warfield/Tychus missions. For the latter three at least, you should be able to complete the missions by going to the mission archive and selecting them from the menu.
Alternatively -- did you do all the available missions before going to Char? If you didn't you'll need to start a new campaign to finish those -- once you go to Char, you can't go back and do any missions you may have missed.
It might be worth it to check your "Wings of Liberty " Achievement progress and list exactly which 4 missions you have yet to complete (The achievements that award Warfield, Mengsk, and uninfested Kerrigan portraits, for reference).
Edit: Okay, it looks like you missed the Zeratul Missions. After completing "The Dig" there is a new item in the Lab screen, in the lower left-hand corner that has "Crystal" or some such identifying it. Clicking it will let you take 4 Zeratul missions. It looks like you only did the first.
