There are certain countries where they can check - and of those some countries that they are more likely to be particularly interested in.
But if you are thinking about countries in Europe, for example, within the Schengen area, they wouldn't be able to track those, since they are in the passport-free zone. So you wouldn't necessarily have to list all travel done within the Schengen area (although, remember that the UK is outside of Schengen).
If you are thinking about trips to the States with private transport, I am also not convinced you have to be super careful.
For major trips, I would really try to be as thorough as possible. It's hard to know how they'd react. I would *THINK* that they wouldn't come down too hard on small errors, but I guess at the end of the day, it depends on the person who reviews your application.
