Here's a YT video by Duracell about how many batteries declared dead and sent to recycling still have some usable energy. In the beginning of the video there's a sequence where they have a row of batteries and a person quickly touches each with a pair of probes to decide whether a battery is worth anything.
The measurement procedure is not documented, but I'd guess they just measure voltage on the terminals. Batteries have likely been idle for days or weeks before the measurement.
Suppose I want to do a similar project and have a pile of batteries and a voltmeter.
What's a reasonable voltage threshold to decide usable alkaline batteries from useless ones?
Answer
A fully discharged alkaline cell (nominal voltage 1.5 Volts) still retains a voltage of 0.9 to 1.0 Volts. Therefore, voltage threshold for measurement can be taken as any value above 1.0 Volts.
Battery energy delivery capacity however would be limited by other factors: Internal resistance / electrode surface deterioration. A cell that has been left unused for a long period would show poor power delivery capability due to this.
One way of evaluating these "depleted" batteries would be to measure current delivered due to a brief pulsed load, i.e. a low resistance across the terminals for a brief duration.
Such a measurement device can be built conveniently by connecting a resistor and a MOSFET in series across the terminals, feeding the MOSFET gate with a series of short pulses, and reading the voltage across the resistor each time the MOSFET is switched on.
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