Leaving stock spare tire when upgarding to bigger tires.

[Beastmaster]

Most open differentials will accomodate a maximum of 1" of actual tire diameter difference.

Limited slip diffs and mechanical lockers (Torsens and Detroit NoSlip Lockers, for example) will take up to 1/2" of tire difference. This is both from practical experience as well as from manufacturer specs. Detroit/Tractech says that for street vehicles with limited slips and Detroit Lockers, the tire needs to be within 1/4".

Anything more than that, the differential will heat up due to excessive wear. If it heats up too much, the diff will literally cook and then spew gear oil.

This is why rotation of your tires is paramount - keep the wear even across all your tires, including the spare.