When vaulting over an object, the character will stop and the animation of drawing a weapon will display, though no weapon is drawn. The only way to fix this is to draw your weapon and replace it.
After vaulting with a weapon in your character's hands, you are unable to remove the weapon by pressing the X in your inventory. If you have the weapon assigned to your quickbar, it removes the weapon from your inventory and drops it on the ground.
If you do not have the weapon in your inventory, you must use an item (food, canteen, etc.) to remove it from your hands. The weapon will then lay on the ground until you are finished with your item, then return to your hands.
While the weapon is on the ground, you may quickly add it to your quickbar prior to finishing your food, but it will still return to the ground, not your inventory when you try to stow it away.