In combat? Nothing, (though Bowls comment about causing damage from removing a weapon makes sense) there are no combat scenarios where a serrated blade is more useful than a non-serrated blade.
Serrations exist to give you more cutting edge so that you can keep an edge longer and were primarily developed for cutting wood.
To effectively use serrations in combat you would have to pull the weapon along your target. This would be completely useless against armor...even if that armor was wooden. Even against heavy fabric serrations would be less effective than a standard slashing blade (katana for example).
In short you would get more blade contacting the target using a standard edge when compared to a serrated edge.
Hold still I need to saw through your protective gear! -- unknown (He died)
Additional note: Having recently picked up forging as a hobby and having started on knives...I can tell you that the grinding/polishing/sharpening process is lengthy and time consuming.
Creating serrations would be even more difficult and the lack of benefit would lead to it being a style choice for the wealthy and not worth the time for mass produced army blades.