Old books we couldn't sell - we'd throw them away. Donations are not necessarily sorted through straight away, and almost always done so after the donor has left the shop, so there'd be no way of tracking down the donor to get them to take them back anyway - unless the donation was Gift Aided, and even then, it's not worth the hassle. Easier to just throw unsaleable stuff into scrap.
Deciding on whether we can sell it - generally, the shop tries to sell books that are in good condition. If the spine is a little creased, it's fine to sell; extensively creased, with damage to covers, then no, probably not sale-able. There is some leeway with certain genres/certain types of books. Sci-fi and classics can be a bit more on the tatty side. There are also some really old books (academic, first editions, etc) that look old, musty and not in great condition but are potentially of interest because of the subject (and perhaps worth a bit more money too) so unless coming apart at the seams, we'd probably put something like that out for sale.
There are two paid employees in the shop I volunteer in - the manager and deputy manager. The manager is full-time, the deputy manager is part time. They're both very nice and I think managing a charity shop can be more difficult and time-consuming than some people might think. The only paid roles the shop has are already filled, so all I can do is volunteer here. Also, volunteering comes with less responsibility and you have some leeway to choose the kind of tasks you'd like to do. Being a paid manager means that you have to do certain tasks.