Is the discard pile public? If I've forgotten whether Mornington Crescent has come up can I look in the pile to check?
This issue has deliberately not been specified in the rules. There are a lot of different groups with a lot of differing views on what degree of memory is appropriate in a game, and I believe it is best for each group to come up with a decision which is appropriate for them.
Speaking personally, when I play On the Underground, the rule I follow is that players are not allowed to look at the discard pile - however if asked I do try to let people know which stations, to the best of my memory, have been visited. However, other groups have the information open, or indeed mark each station when the Passenger visits it, and I think that these options are also perfectly fine.