The biggest ones by far is the lack of a carbon tax and, as a sibling comment notes, not having to pay for the health effects of their product. If you factor in the likely costs of climate-induced deaths, the total costs will be almost certainly be more than the total value of all fossil fuels ever extracted. The lack of these costs is therefore the ultimate subsidy in that the entire global industry, and in a sense all human civilization as currently constituted, is premised on keeping these costs unaccounted for. Presumably this is the kind of thing you mean by "specious" though.
Still there are lots of carve outs for the way extraction equipment and other capital costs are accounted for in tax law that are effectively direct subsidies to the oil industry. These won't end the practice of fossil energy use like ending the big ones would, but any little bit helps. Would also be nice to stop leasing out government land to do this incredibly destructive thing with it -- at least make drillers own the land or lease it from a private owner.