Something similar to your story happened to me once (not at the same
station), so I'll have a go at explaining it. I was at the
exiting-the-gates part of an out-of-station interchange, and ended up
getting charged triple (charged separately for 1st half of journey,
"incomplete" journey that never took place, and 2nd half of journey)!

Another one to add to the catalogue of Oyster problems and oddities... I
got my friend an (unregistered) Oyster to use when he comes to see me
occasionally after work. He made a journey from South Harrow to Fulham
Broadway, but had a problem getting through the gates at the end - he
went to see the station assistant, who apparently tried his card on the
side gate,

I do wish they wouldn't do this - it leads to all sorts of incomplete
journeys and broken out-of-station interchanges.

and told him he hadn't touched in properly at South Harrow.

I had a look at the journey history on a ticket machine later, and it
showed the following:

£1.10 Fulham Bdy
£1.80 S Harrow - Fulham Bdy

...which I reckon was because either credit had been deducted from the
card when he first tried it on the gates and the card then registered a
"touch in" when the SA tried it, or the SA accidentally touched it twice.

Assuming the journeys are in reverse chronological order, what I think
happened is that when he touched out at the gates, it registered the
journey as usual and the money was deducted, but for some reason the
gates didn't let him out. This may be because he was following someone
through the gates whose ticket was rejected (so they went through on
"his" gate opening), although when it happened to me (the gates closed
on me for no apparent reason as I went through them) I'm about 80%
sure that didn't happen. At any rate, if this happens, then the exit
gates refuse any additional touches-out, forcing you to go to the SA.

We went to the ticket office at Fulham Bdy to try to sort it out, but
the member of staff there wasn't very helpful - he couldn't seem to see
the £1.80 charge and thought my friend had only been charged £1.10, and
advised him to keep quiet about it if he were him!

When it happened to me, the very helpful gent at the ticket window
tried to cancel the erroneous journeys, but the system would only let
him do anything to the most recent one. (A separate experience of an
Oyster problem at a different station suggests that this happens
everywhere.)

We later phoned the Oyster helpline, who told us that they couldn't do
anything about it because the card wasn't registered (!).

Same with me - after holding for almost 20 mins, I spoke to a lady who
took my Oyster card number and a brief description of the problem
(extra jouneys for which I got overcharged), acknowledged my card was
unregistered, and got me to explain fully. I then spent several
minutes explaining exactly what happened (well I suppose she was
getting paid for it), after which she politely told me to sod off as
she couldn't refund anything as my card was unregistered!

I finally tried Gloucester Road station later, where the member of staff
in the ticket office was much more helpful, but still couldn't resolve
the problem, and suggested we phone the helpline.

I was more annoyed that the helpline said they couldn't do anything,
than that the unresolved journey got onto the card.

What really annoys me is that ticket office staff don't have the power
to correct more than the last journey that appears on the card. I
don't see why I should have to spend ages on the phone to an 0845
number to get it fixed (and then only if I allow TfL to associate my
name and address with my every movement) - I should be able to get it
done there and then.

I'm usually very
forgiving but it strikes me as odd that it's OK for LUL not to refund an
overcharge when the card is unregistered, although perhaps there's a
good reason for it.

Perhaps there is.