Q: How would you test the word count program? What kinds of input are most likely to uncover bugs if there are any?
A: There is no perfect answer to this kind of question. Writing good test is really a matter of experience. Part of the reason all programs have bugs is that even the best test writers can't anticipate all the wild ways a program will be used by other people. Nevertheless, writing good tests is a good skill to develop, as you can filter out about 99% of potential bugs that way, and prevent unexpected behaviour when you make small changes to large programs.
The first thing I would do is test it with no characters at all, hoping for '0 0 0'. Next, test it with one word, then with one tab, then with one newline. Then a tab and a newline, then a newline and a tab... you probably don't need the full 16, but instinct tells me that starting input with white space might cause problems. After that, a few short strings like 'two words' will cover the basics. Of course, in real life, I hope I can write such thorough tests.
That might seem like a lot but if you write a test once, you get the peace of mind forever.