How to make apostrophes appear normally when copy-pasting from a MS Word document?

Word auto corrects input ' to the typographically correct ’. LaTeX does this, too.

1. You can try to search-and-replace all ’ to ' in Word itself or
2. Use another input encoding, for example UTF8: \usepackage[utf8]{inputenc}

I have had such problems too. To me it seems Word does dark replacement magic with all kinds of special characters that are neither "," nor ".". What exactly it does seems to depend on language settings and Word versions.

I'm using my own voodoo to deal with that, amongs which is this sed-script

#!/bin/sed -f
s/\x84/,,/g
s/\x93/''/g
s/\xE2\x80\x98/'/g
s/\xE2\x80\x99/'/g
s/\x85/\\ldots/g
s/\x96/--/g
s/\xE2\x80\x9C//g
s/\xE2\x80\x9D//g
s/\xE2\x80//g

For your purposes the first 4-5 rules should be the most interesting. As always, YMMV.