Can I skip to the next campaign mission without completing the current one?

One of OFP's built-in cheats will let you do this but at a price. While in the campaign mission, hold down your keyboard's left SHIFT key and then the numeric keypad's minus ("-") key, release them and type the word ENDMISSION. This will allow you to progress to the next campaign mission should you get stuck, begin to pull your hair out and want to move on.

So what's the price? By using the ENDMISSION cheat, OFP will add a penalty to your stellar record. In the 1985 Cold War Crisis Campaign, this could eventually lead to your dishonorable discharge by Colonel Blake.

For an alternative solution, look here to see how you can play any mission within the campaign.