A Vertical Speed Indicator indicates rate of altitude change. Traditional VSIs use a calibrated leak to measure the rate of pressure change, and therefore the rate of altitude change.
However, pressure does not change uniformly per altitude: in a standard atmosphere, air pressure at 0 MSL is 29.921 inHg, and at 1000 MSL is 28.856 inHg: a 1.065 inHg difference. But 10,000 MSL is 20.577 inHg and 11,000 is 19.791 inHg: a .789 inHg difference. A calculation suggests that a VSI calibrated for sea level and climbing at 1,000 ft/min would indicate 739 ft/min at 10,000 feet.
The airspeed indicator has a knob to calculate true airspeed based on altitude and temperature, but the VSI has no pilot-accessible controls. Glass panel instruments would presumably handle this automatically, but is there any correction for altitude in a steam-gauge VSI?