Explanation on when the possessive should be used instead of an attributive noun

Solution 1:

All of your examples have something in common: though some of the attributives that you give have the form of noun phrases, they are all primarily adverbial in usage:

• Today we're watching the news.
• This week we have to make a schedule.
• Tomorrow we should have lunch.
• This year they gave a good report.
• We visited there last summer.
• She had the records of the meetings last year.

These adverbial phrases have limited currency as nouns. You can sometimes use them as the objects of prepositions, as in Before yesterday I had never heard of her, or as the subject of a sentence as in Today was a good day. However, they don't show the full range of syntactic variation that ordinary noun phrases do: they can't be pluralized and they resist being used as attributives. As your examples show, if you want to use an adverbial in this manner, you're required to mark it with the possessive -'s.

Solution 2:

I suspect the confusion is more dependent on culture than language. Germanic (at least, probably other cultures as well) thinking allows an inanimate object to have 'ownership' of other objects (animate and inanimate.) I use 'ownership' to mean a relationship that has special importance.

Today's news

The events that occurred today 'belong' to today. Yesterday cannot claim 'ownership' of the events of today.

The previous class's students

Obviously, a class cannot actually own a student, but the students belong to a particular class--i.e. there is an extra-special relationship between the students and the previous class.

All of the examples in the original question were related to time ownership--a particular period of time having ownership of an object (physical or non-physical.) It's possible that the confusion is due to the way time is perceived. Germanic thought sees time as linear, therefore a given event or object can exist only in a single period of time. If an event repeats (eg. solar eclipse), it is seen as a different event than all other previous events having the same properties.

Another possible point of confusion could be the method of categorization. When considering 'vacations', what kinds of vacations can we have?

• Bus trip vacation
• European vacation
• Working vacation
• Summer vacation
• Summer's vacation
• Summers' vacations
• Last summer's vacation

In Germanic thinking, a bus trip cannot 'own' a vacation, 'bus trip' is a kind of vacation. In the same way 'summer' is a category of vacation, but 'summer's' vacation is that vacation-event that occurred during a particular summer.