I extensively use Acrobat for academic research. The fact that when I search for an expression it highlights all its occurrences throughout the file is interesting.
It would be even more interesting if I could highlight several searches at once, and colour them differently.
Those searches would be available on a side panel allowing me to select the colour for each expression, delete them, add new, etc... more important, the searches should be persistent and stored with the file when I close it.
It would also be interesting if searches, upon flagging them as such, would operate cross file.
For example, when looking for the name of one same author quotes in different papers I could have an overview of how many times and on which of the open files their name (basically a text expression) appears.