Holes, slashes. Cut a patch about 3/4" larger in all dimensions than the hole. Feather edges with a razor blade. Apply a thin layer of Devcon Patch glue and smooth down.
Felt loose from wood. Clean off old glue. Apply a thin layer of Elmer's Glue-All to felt and smooth down.
Felt loose from glass, ceramics, metal, plastics, etc. Clean off old glue. Apply a thin layer of Plio-bond cement to both surfaces. Let dry until tacky and press together.