I've found an odd discrepancy in the Fire Elemental's ability to set "stuff" on fire.
In the Fire Elemental's statblock in the Monster Manual, the description of the Fire Form trait states (emphasis mine):
Fire Form. The elemental can move through a space as narrow as 1 inch wide without squeezing. A creature that touches the elemental or hits it with a melee attack while within 5 feet of it takes 5 (1d10) fire damage. In addition, the elemental can enter a hostile creature's space and stop there. The first time it enters a creature's space on a turn, that creature takes 5 (1d10) fire damage and catches fire; until someone takes an action to douse the fire, the creature takes 5 (1d10) fire damage at the start of each of its turns.
This is all well and good, and means the Fire Elemental can wreak havoc on large swaths of enemy creatures as it moves through them. It would also appear that this would set both friend and foe on fire, since there's no distinction in the description of creatures.
However, there's no mention of objects until we get to the Fire Elemental's Touch attack (bold for emphasis mine):
Touch. Melee Weapon Attack: +6 to hit, reach 5 ft., one target. Hit: 10 (2d6 + 3) fire damage. If the target is a creature or a flammable object, it ignites. Until a creature takes an action to douse the fire, the target takes 5 (1d10) fire damage at the start of each of its turns.
By RAW, it would appear that while Fire Elementals can ignite and damage lots of creatures by moving through them, the ability to set objects on fire is limited to Touch attacks only. This seems odd, as its fire does affect both friend and foe.
Am I right that its ability to set objects on fire is limited to objects targeted by its Touch attack? Or is this a grey area where the failure to extend this to objects is an oversight in the rules?
Additionally, if for some reason its Fire Form trait did affect objects, wouldn't that mean that it sets fire to every flammable object it moves through?
(Worth noting: This question has (sort of) been asked before, but for Pathfinder 1e, not D&D 5e.)
Best Answer
Your assessment is correct, the rules say that Fire Form only burns creatures, while the attack burns objects too. RAW, that's as far as we can go.
Keep in mind the description also says;
So while we have no explicit rules, it does fit the narrative. Just like a giant could bust through a fence and a flapping dragon could blow your laundry off the line, we don't have rules for everything - the DM is expected to fill in the gaps.