"there is a man/woman ICON - click it. It is supposed to show "Marriage facts, notes, and media" - and it does not"
There are two facts that are available on the resulting screen when you do the above operation. The first fact is the marriage fact and is a Tab at the top of the page.
The other fact is available in the pane on the right of that window below the Statistics. There are two tabs Sources and Notes. These notes area the same as you would see if you went from People Person ''"Shared Facts with ..."'
I have not been diligent in following this, but I interpret "Shared Facts with ..." as being those facts associated with the source. ie names are misspelled in the record. and Marriage Facts are those associated with the marriage. ie John and Jane were married in their parents house.