All tubes degrade with use, and one of the ways this happens is by developing high resistance leakage paths between the elements and through the heater-cathode insulation. Most of the time, tubes get replaced for other reasons before these leakage paths get bad enough to become troublesome. On the other hand, if there are hard-shorts in a tube due to loose or deformed elements, the problem can't get any worse!
If you turn to the chart on page 4-4 of the TV-3 manual
http://www.mcmlv.org/Archive/TestEquipment/NAVSHIPS91254-TV-3U.pdf (Courtesy MCMLV.org), you'll see a chart that can be used to determine which elements are causing the shorts light to come on. Heater to cathode leakage may be tolerable in output stages, but I would stay away from any tube that shows leakage from any element to the first grid.