I have understood that an AR (in a standard diagonal) should carry the flag in his or her left hand to be closer to and more visible to the referee, then transferring it below the waist to make one of the many right-handed signals. (With the exception that when running towards mid-field while not side-stepping, the flag should be in the right hand, again so it is more visible to the referee.)
I have heard rumblings of a limited change to that procedure by which the AR would carry the flag in the right hand when moving side to side alongside the penalty area. The rationale, I understand, being that more signals are made with the right hand so the signal can be made more quickly.
So my question is which the current proper procedure is — or is either one acceptable?
USSF answer (October 4, 2010):
There is no directive requiring the method you suggest. However, we can offer some advice on the matter.
First, if the referee directs the AR to follow this mechanic, then do it because it is just a mechanic and therefore an assessor, asking the AR why he was doing this, would (reluctantly) accept the “Nuremburg defense” (i. e., “he told me to do it” — “he” being a person in a position of authority), but then the assessor would proceed to grill the referee.
Second, it is arguably a mechanic which replaces an existing standard procedure and thus is not allowed in the Guide to Procedures (which you can find at this URL: http://www.ussoccer.com/Referees/Referee-Development/Instructional-Materials.aspx).
Third, it is possible that you have misunderstood the emphasis — namely, that several of the flag signals performed by the AR down that close to the goal line are signals for offside, goal kicks, and corner kicks, and they ARE recommended to be performed with the right hand (although so far only the requirements for pro match referees have insisted on using the right hand). In most of the games we do it doesn’t matter that much.
Fourth, the emphasis for the last several years has (rightly) been on “getting it right” and not on “getting it done quickly” so the alleged need for a quick signal is not persuasive.
And finally, this is the sort of thing that needs to be discussed at some length in the pregame conference among the officials on the game.