What is the mechanism for the double bond migration in 4-methylcyclopent-2-en-1-one?
After Step 2, re-protonate alpha to the carbonyl (the double bond has now migrated to the beta-gamma position).  Now enolize the carbonyl - remove the proton next to the methyl group (the top one), then push the electrons all the way back, protonating the gamma position.  Job done!