I believe it's the referee's decision whether to swap the linesman around at half time. I remember reading an article by a referee saying he always did, because it meant each linesman was in front of another set of fans, so if he was getting stick from one set, he got away from them in the second half.
Personally I also think it should be mandated that they stay where they are, as some are much more likely than others to raise the flag on marginal decisions.
At the time of the disallowed goal, I thought Ward was well off-side, but looking at the replay he timed his run perfectly. He was level with the defender in shot, and there was also a defender out of shot with whom he must also have been pretty much level.
I have a memory that Ward had a couple wrongly disallowed for off-side last season too. He makes short, fast runs which have to be timed perfectly, and it seems to leave him prone to this sort of misfortune.