1. This is a broad assumption. "this means she would have had several fake passports." Make this a "should". I have checked so often into hotels that either did not check my passport or did not look at it.
2. 70ies passports were easy to fake. In fact, I knew somebody who "professionally" faked and manipulated passports to help people escape from the GDR (East Germany) when he was a student.
I think, especially for a foreign woman in small Norwegian places in the 70s, that people would check passports.
And yes, 70s passports were easier to fake. Still, if she had multiple fake passports, as well as with the circumstances from the article, I have a feeling that this isn't just some independent person playing spy. Using a fake passport to escape the GDR makes sense: that's something a non-spy would do. Using multiple fake passports to check into hotels in a foreign country, meeting with Germans in Norway, evading detection, then getting killed by someone who knew what they were doing? That doesn't sound like a non-spy.
But yes, the problem here is that if each of my assumptions has a 10% chance of being wrong, and I make 5 assumptions, my final categorization has about a 60% chance of being correct. Still, it can put the search on the right track: searching a small list of people (short female aged 25-40 that was a USSR, GDR or BRD spy in the year 1970 with gold teeth and brown eyes) makes the search a hell of a lot easier.
I was several times in the situation that I had to check into Hotels without a passport or with "modified" data (don't ask). It is nearly always possible. Even in CHINA I was able to stay into hotels without a ID/passport. Something that should not be possible by law.
"Still, if she had multiple fake passports" You phrase this like a fact. If you tackle such a problem the right thing would be "she might have had..". You can never take such information as "proven facts". If I would assign something then: a 50% chance that she had faked passports.
Also, spies normally don't use so many different passports in the same country. Looks odd to me.