The disadvantage of elective mode is that it makes it much easier for you to make some really poor skill choices.
Another disadvantage of elective mode is that it allows you to accidentally drag skills off your action bar. EDIT: Please note that as of patch 1.0.4, skills can only be dragged off the action bar when the skill menu is open, preventing this from being an issue moving forward.
The idea of the "non-elective" layout is to help guide new players into taking balanced builds, that incorporate a good mix of primary offense, secondary offense, defense, and utility.
For example, in elective mode, a wizard could choose to use no signature spells. This means that once they run out of arcane energy, they'd have to resort to melee. While melee builds for wizards are viable, ones that involve swinging a weapon with no arcane skills boosting damage are going to be less than optimal.
The advantage of elective mode is that it gives experienced players much more flexibility in their skill builds, and gives the freedom to try some unusual, but potentially viable, builds.
As James has pointed out, it also allows you greater control over the binding of keys/buttons to skills, letting you use setups that may feel more natural or easier to use than those imposed by the non-elective version.
Best Answer
The other answer is not always correct. Some skills use only the main hand weapon damage: see here or here. These tend to be skills that fire infrequently, possibly with long cooldowns. If those skills fire less frequently than the slower weapon, attack speed is irrelevant. Only weapon damage matters. For those skills, you are better off having the weapon with the higher damage in your main hand -- even if it has a lower damage per second (DPS).
Note: in most cases, the other answer should be correct. Most skills alternate hands. Only particular builds are affected at all and they are only impacted when the relevant skill is used.