Well, I did the crossword on line as usual, put PERSONAL as the answer, submitted it and was informed that I had one incorrect answer. Annoying, it doesn't tell you WHICH answer(s) are incorrect. I'm pretty sure of all the others, so I reckon it's this one.
The clue on the online version (which has been known to be slightly different from the paper version) is:
A child, almost completely offensive? (8)
The pattern is ?E?S?N?L so, if it's not PERSONAL, it must be SEASONAL which doesn't fit in any way that I can see.
The "known" letters come from
17a HIGHLAND CATTLE
20a TV DINNERS
24a VEGAN
28a MARSHAL