It looks like the following advice by Stefan Blom resolved this issue:
"... change the Display for Review drop down from "Simple Markup" to "All Markup" on the Review tab."
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However I am not 100% sure about it.
Last week comments/tracked changes behaved differently.
I was able to see tracked changes but was NOT able to see Comments.
Also "Previous" and "Next" icons under "Comments" group were disabled.
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Today when I have repeated the same experiment on a new file, I noticed different behaviour.
Even when I used "No Markup" option, "Previous" and "Next" icons under "Comments" group were enabled.
So it looks like I can't reproduce the same issue using a new file.
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I assume that the file I used last week was corrupted somehow when opening in Word 2013.