No problem with pushing the reset like you mentioned. Pushing it just manually pops the bi-metal discs back into the closed position (or does nothing if it was already closed). Checking for a grounded element requires an ohm meter (i use analog for simplicity, but hard to find now). The heater must be full of water. Turn off the power, remove the wires from both elements. With the ohm meter in the continuity mode, put one lead to one post on the element, and the other lead to the metal of the tank. Scratch the metal a few times with the second lead to ensure a good contact. If you see the needle move, (or otherwise see "continuity") the element is grounded. Repeat the drill on both studs of both elements.
What does "grounded" mean? The outer sheath of the element has cracked and water is now getting inside the element to the filiment. It will work like this for some time. The problem with the grounded element (aside from a potential shocking problem) is that the element is now able to heat the water with 120 volts (normally takes 240). This is the second most common reason for a tripped high limit. A bad lower stat is #1. Others have suggested replacing the stats in pairs when there is a problem. I agree 100% with this theory. If in doubt, replace them both and be done with it.
And I always laugh when someone says they can use a meter to check the stats. It's impossible to check the stats with 100% certanty. Even the "heat it up" trick isn't reliable, because the act of removing the stats from their holders will oftentimes break the contact loose that had stuck closed. I like to prove the things I can prove ( elements are not grounded, and are drawing amps under voltage), and then proceed to the obvious conclusion.