There are 3 methods to take notes:
1. Hi-tech notes: using computer / tablet / mobile you mentioned it in your question.
2. Pen and Paper: Widely used but not recommended because you might miss some issues the user experienced while you are busy noting them down.
3. Record and analyze: keeps you focused, gives you an option of watching it n number of times - recommended.
If you've ever observed a usability test, you'll know that it's often
hard to keep up with the tempo of what's going on. Nothing seems to be
happening — and then suddenly a handful of usability problems appear
at once. It seems impossible to get them all down: you write down one
usability issue, but that prevents you from observing the next
problem. You look at the participant — who is now struggling with a
different problem — and you wonder how the participant got here and
what you've missed. If you have the job of moderating the session and
taking notes, it's even more difficult: how can you focus on the
participant and take notes?
So it's no surprise that many people think the easiest solution to
this problem is to use James's approach. Skip the note taking and just
review the recordings, or alternatively just note down the key issues
after each participant has finished.
This article Note taking during user testing speaks more on these methods. And usability.gov has a great document on Note taker's guide