I want to get some practice and build more appreciation for the use of stacks in the context of classical moduli spaces of sheaves. Here by classical I vaguely mean hands-on description of the geometry of moduli spaces of sheaves in the spirit of work of Drézet-Le Potier and the book of Huybrechts-Lehn. Two great papers I've read so far which use stacky techniques are Walter's "Irreducibility of moduli spaces of vector bundles on birationally ruled surfaces" and Göttsche-Hirschowitz's "Weak Brill-Noether for vector bundles on the projective plane".
Can you recommend me more great papers using stacks to prove things about moduli spaces of sheaves?