Zootierliste in general is a fairly reliable resource, though over the years it has grown to be quite notorious for the inaccuracy of its UK listings with a lot of people trolling and making up species that zoos don't actually have; however, this would of course have the reverse effect of what you're saying has happened with Twycross.
Another thing I'd say is to always check the source. You can do this by clicking on the zoo's name under whatever species you're checking, and looking under 'Quellen/Nachweise.' The most common type of source is of course someone's visit, which will read: 'Besuch' (visit), followed by the date of the visit in question, and then in brackets, either 'gesehen' (seen) or 'nicht gesehen' (not seen), followed by either 'ausgeschildert' (signed) or 'nicht ausgeschildert' (not signed).
If a species is neither seen nor signed, then they are likely either offshow, or gone from the collection entirely, but the editor just didn't feel as though they had enough evidence to move it to former holdings. If the date is old, then depending on the lifespan of the species in question, and on if you have any contradictory information of your own, then take it with a massive pinch of salt. However, if the source is recent and is listed as both seen or signed, then 99 times out of 100 it is correct.
The other thing is with subspecies. Sometimes zoos get listed as holding certain subspecies-pure animals, when in fact they are more likely to be generic hybrids, just labelled poorly by the zoo itself. Also, ZTL sometimes has duplicate listings where an animal was counted as both its subspecies and the non-subspecific, general listing (e.g. 'Asian Elephant' and 'Sri Lankan Elephant').