I play UFO Defense / Enemy Unknown (X-Com) since its out now. And I always equip a weapon on the right hand slot and a grenade in the left hand slot.
On most Longplay videos, people equip grenades on the belt and take them from there when needed (which costs Timeunits)
Why is this? Is it influencing the aiming or timeunit use of my soldiers to have a weapon in one hand and a grenade in the other?
According to the UFOpaedia, having an item in your off hand when firing a two-handed weapon reduces your accuracy by 20%: