Travel history is made available to those who register their Oyster Card online, and only becomes available the following day. So you won't be able to check when you are in the middle of a journey. If you haven't registered your card, you can still view the last 7 days history.
You can check the online journey history for previous days and look for Incomplete journeys.
More on Incomplete Journeys here:
If you don't touch in and out
If you're using pay as you go on Tube,
DLR, London Overground, TfL Rail or National Rail services in London
and don't touch in or out, you may have an incomplete journey and be
charged a maximum fare of up to £8.80.
If you have an incomplete journey we don't know where you started or
ended your journey meaning we are unable to charge you the right fare.
When you touch in at the start of a Tube, DLR, London Overground, TfL
Rail or National Rail journey in London, we deduct up to £8.80 from
your pay as you go credit.
When you touch out at the end, we work out the right fare for your
journey and the amount deducted from your credit is adjusted.
If you don't touch in and out correctly, we don't know what to charge
you, so a maximum fare of up to £8.80 is deducted from your credit.
Maximum fares don't count towards capping and don't apply on buses and
When stations are very busy we may leave the gates open to control
crowds and ensure that people can leave the station quickly and
safely. If so, you might not be able to touch out but we'll aim to fix
this for you when you touch in to start your next journey.
P.S. Technically you need an address to register your Oyster Card, so Tourists are officially advised to use a Visitor Oyster Card.
P.P.S TFL is planning to replace Oyster with Contactless Payment Cards anyway, which according to @ecatmur you can check your Dashboard (requires registration) to get up to the minute updates.