Thanks everyone. I don't have an Aldi near me but will try the Lidl ones, or Tescos own (avoiding the lemon variety). I used the Fairy ones becasue they had a Which? award on the front, so I guess I have been a slave to marketing. Also because a plumber friend said they were the best, but I'm sure own brands work just as well, and yes I do rinse the worst of the muck off first if it's ground in. But I do not go "full Monica" on them, like my sister does, and pretty much washes them clean before they go in the dishwasher!
I don't think I'll bother with salt.
The trapdoor mechanism has always worked fine for me, but I remember my ex had trouble with hers where the tablet would not eject properly and you ended up with half digested tablet gunk in there.
Apparently, by design one should lob the tablets in the bottom of the dishwasher chamber; the trap door thigummy is designed for powders.