watched my friends swim vs watched my friends swimming

(Grammar Questions I Couldn't Answer)

This also relates to the same sentence I published in the previous post.  (We got a few different questions out of this sentence.)  The original sentence was:

In the summer, I looked at my friends swim at the pool and I wished I would be able to do it.

Now, to me the big problem with this sentence was that looked at needs to be changed to watch.  But once that was done, I was fine with it.

In the summer, I watched my friends swim at the pool.

My students, however, thought that we should also change "swim" to "swam" .

No, I explained, it's good like it is.  It can take the bare infinitive form after "watched" .  "Watched" holds the tense here.

But, my native speaker intuition was also telling me the sentence could be either "I watched my friends swim" or "I watched my friends swimming".  So what would be the difference?

And then I realized I had had a version of this question twice before:
"hear us sing" vs "hear us singing"

and

I saw her cry Versus I saw her crying