LP combustion is very clean. Some particles and exhaust gases, like carbon monoxide, are created, but these are vented up through a pipe connected to the system and do not linger in your fireplace. Over time, you may notice soot creeping over your log. This is caused by trace particles that are left behind and is a normal part of the process.
If you notice excessive amounts of soot staining the walls and glass of your LP fireplace, you likely have a problem. When the flames cannot burn hot enough, more soot is created and left behind. This indicates a lack of air flow in your fireplace, potentially caused by vent clogs, improper damper remodeling or other issues that need attention.
The other side of the air flow issue is gas flow. Your LP fireplace needs a proper gas/air mixture. If the air flow is proper, the problem could be caused by gas flow. Gas flow that is obstructed by valve problems can lead to soot, as can excess gas flow. This can be controlled by adjusting the valve controls on the front of your fireplace blower.
Vent-free fireplaces are designed to burn LP gas so cleanly that all exhaust is burnt up and there is no need to vent anything. These furnaces should be almost completely soot free. If you notice soot building up in a vent-free fireplace, shut it down immediately and call a professional to examine the system.