As others have said, you need to take the crank off and see exactly what is happening. If it is the bottom bracket shell not being faced, the best thing would be to get it faced, since you are having an issue with it backing out.

Truth be told, I bought a frame in 1990 and the non-drive side needed facing. I am ashamed to say I elected to install the bottom bracket and see how things went. The bottom bracket was a specialized with sealed bearings. I have replaced them without a problem. Need-less-to say that when I replaced the crankset this year I was faced with the same dilemma, and resorted to placing a spacer on the non-drive side. So far so good.

Against the correct advice, you might be able to take a spacer and angle it to square things up. But 1mm is quite a gap. But this is not great advice.

John