Note: This started as a comment. It's morphing into an answer. :)
You are right. (I think...)
I think some people may be getting hung up on your ambiguous sentence example. That's not really an issue, right? I mean, it's obvious that one can construct ambiguous sentences, and I think you know this, but that's not what you're really asking. I think you're stumbling because you don't fully understand your own question. That is, you're formulating the question wrong because you are confused.
I think (you can confirm) you were using the ambiguous sentence to try to illustrate your main point (DEF1) which is that the Logman dictionary is confusing when it supplies nearly identical sentences to different meanings. I think you are right that the dictionary is not helping to distinguish the finer points (DEF6) of the definition of point. Furthermore, the dictionary might be misleading.
Here's another way of looking at it. Suppose I have two sentences:
- I have one more point to make. (DEF1)
- The car's best selling point is it's price. (DEF6)
In the above two sentences, different denotations of point can clearly be identified.
But given the two example sentences that you indicated, it's difficult to see how one is a different denotation than the other. If there's some distinction for finer points of world politics and finer points of various cars it escapes me. Sure, one is about "politics" (which is ideas) and the other is about "cars" (which is concrete). But it would be a use-mention error to ascribe a denotation to point based on the topic of discussion. One can surely make points (DEF1) about cars, politics, and anything else. I would be happy putting both sentences under DEF6.
The following is an extract for DEF1 and DEF2 from Logman Dictionary online.
Logman Dictionary of Contemporary English: Definition of point):
Both definitions contain the same sentence:
- Example sentence under definition 1: