Dave,
If when you touch your meter leads together you get 1 ohm, you are measuring your meter lead resistance. That should be considered zero ohms.
Is your meter one where you select the resistance range or does it "autorange?" This can make a difference if you have to select the range.
The terminals with * usually are either high resistance or connected to a capacitor that will charge ending with a very high reading. Some meters will say "OL" some will say "HI" some will read "--". The problem is that different meter manufacturers give different indications.
These * terminals are not critical that you get a definite reading. But, as mentioned earlier, the power supply capacitors will be ruined if put in backward. The diodes are another thing to triple check.
Terminal 12 is the power supply ground, as are almost all of the terminals you get a reading of 1 on. T12 should give you good resistance readings and should be grounded to the chassis at terminal 3. I had to look through the manual quite a bit to find the grounding point. Maybe try your meter grounded at T3 and consider 1 ohm zero ohms.
Look in your manual at page 22, the middle picture. There is a black wire that ties all the audio signal grounds and power supply grounds to terminal 3. If it is not properly soldered you don't get ground on anything else. Measure resistance from the lug with the black wire on it (in the manual, I don't know if you have the same wire in the kit) to the chassis. It should be near zero ohms.
I am pretty sure your grounding problems are here.
FYI, the circuit common/ground starts at the top plate at terminal 3, goes to volume pot left hand lugs (as you look at it while assembling), to the 1/4" headphone jack lugs closest to the top plate, to T12, to T14, to T20. It may seem to jump all over the place but it is one nice clean sweep from T20, the power supply grounding point to the RCA Jacks outer conductor brought to the volume pot.
Every one of these terminals get their ground at T3.
