I would like to be able to buy an Oyster reader (similar to that used
by inspectors) so I can check that my Oyster has been processed
correctly after boarding a bus or tram.

The problem is you have no proof that you have paid - at least if I had
an Oyster reader if I see a problem with my card I can try to validate
my Oyster Card again.

OK it may be a dumb question, but I don't have an Oyster, but have seen them
in operation a lot. Ok I put a £10 credit or whatever on this chipped card
and start using it- it doesn't have a display on it, neither does the
reader, how do I know the remaining credit... It just seems odd that I could
have a valid oyster on the first part of my journey, which has 'expired' by
the time I get on the bus to make the last part of a journey...