For voltage issues, first check the double pole breaker, they can trip without looking like they did and they go bad also. Check each pole of the breaker with your voltage meter from the hot wire hooked to the breaker to the neutral/grounded bar in the main panel. Each pole should have 120 volts.
Elements can have generally 3 problems, shorted, open/broken off, or gunked up with minerals in your water which reduces their effectiveness. Check the elements for proper voltage, resistance and continuity with power on and off according to the instructions with your voltage meter(I don't recall the exact procedure). Run some hot water to see if the bottom one turns on and later as more hot water is run, the upper one should kick on. If you have an ampprobe, they should pull about 18 amps. If you remove an element to check it out make sure the power is off before you drain the water or else the elements with fry without water(refill it before tripping the breaker to reenergize the circuit). Generally replace both elements if that is a problem.
If the elements are ok, then you could replace both thermostats. The thermostats will operate independently and not always be on in unison.
Check your dip tube by romoving the water inlet and pulling out the diptube which should go down to the bottom of the tank. A part or all of the diptube being broken off could account for not all the water heating. Pieces of white plastic in your faucet aerators would be indicative of this. Your water heater is old enough that the diptube is subject to recall and replacement. Go to the website for diptube settlement that lists the brands and their serial numbers that are recalled at www.diptubesettlement.com
Look for bleed over or leakage of hot to cold at a single handle faucet even if the faucet is off.
Did you test the temperature at the water heater drain cock which may be more accurate.