I own a Texas Instruments 101. Mine works fine, but if the button is indeed contacting the tab and jumping to the date, then what I would try is taking the module out of the watch case, and try using something steel to active the button out of the case to see if it has something to do with the case enclosure itself. In other words...
1) module out of the case.
2) Put battery in battery well with a steel backing to close the circuit.
3) Try using a steel pin or a steel screwdriver to check the time/date.
If the same thing happens (time shows really fast, then the date jumps in) then the problem is with the module, but if the time displays normally for just 2 seconds, and disappears, then is is the buttons or the case if the Texas Instruments 101 watch. If the latter happens you may have to take the buttons completely out of the case, and clean the port where they fir, and the buttons themselves. I have never done this with LEDs, but I have done it with about 7 front-button Seikos.
Anyway, let us know how it turns out.
- Patrick