The disadvantage of not wielding a shield is your armor rating goes down as much as the shield's rating (and whatever additional boost it may have). Shield's are especially useful at close quarters combat, bashing an enemy gives that crucial second or to to land a critical hit. Unless you intend to saturate your enemies with fire and frost spells at a distance, a shield is essential.
I find this combination useful: Dual wielding is best for light armor. Shield + Sword for both light and heavy armor. Two-handed weapons for heavy armor (the heavy armor compensates for the absence of the shield, and my two handed weapon have a block bonus). I rarely use Spell + Sword combos, hence my magic hasn't really gone up. Mages have a disadvantage, unless one makes a heavy armor with magic bonuses.
If there are 4 or more enemies, I always snipe first and thin the herd down (or at least, get their health down significantly), before coming in with 2H sword. In dungeons, 1-hit sneak attack with Mehrune's Razor is the best.
Is there a way to get back the Unbreakable Lockpick?