In this F-104 V-n diagram, why does the stall speed (in terms of IAS) decrease with altitude in some parts of the flight envelope?
As an airplane approaches Mach 1, all pressure changes grow with the Prandtl-Glauert factor of $\frac{1}{\sqrt{1-Ma^2}}$. Therefore, the lift curve slope increases so the wing produces more lift at the same angle of attack and dynamic pressure the closer its Mach number is to 1. On wings with thicker airfoils and higher aspect ratio the maximum lift coefficient drops in the transsonic region; however, thin wings of low aspect ratios are unaffected by this.
NACA TN 3469 by Edward Polhamus compares wings with varying sweep angle, thickness and aspect ratio. The plot below shows that the Prandtl-Glauert effect is strongest for unswept wings and the transsonic lift bucket disappears for thin wings with an aspect ratio of 4 and lower. The F-104 had a 3.36% airfoil and an aspect ratio of 2.45.

This effect also shows up in the maximum lift; the plot below is from Sighard Hoerner's Fluid Dynamic Lift, chapter 4. It shows how the Mach number affects maximum lift: Small leading edge radii show a loss of maximum lift at moderate Mach numbers but perform well at transsonic speeds.

The indicated stall speed decreases with altitude because the lower temperature lowers the local speed of sound and brings the airplane closer to Mach 1 and thus to higher maximum lift. This effect is limited to subsonic speed close to Mach 1 which explains why those corners only show up when the indicated airspeed correlates with Mach close to 1 at that particular altitude.