What skills don't reset Sharpshooter?
I know that Vault (Trail of Cinders) does not reset Sharpshooter, so after a while it always crits. Are there other skills that don't reset Sharpshooter?
Currently in 1.04 the bat and sentry do not reset the sharpshooter bonus but do benefit from it. I think dots like jagged spikes and trial of cinders were hotfixed not to make use of the sharpshooter bonus. In 1.05 these mechanics will change: pets and sentries will not be able to crit anymore :(
Caltrops#Jagged Spikes certainly does not reset Sharpshooter, and certainly does benefit from it. This is the primary killing skill my DH uses, and I've re-tested it with every patch. It still works.