On the day, dead annoyed about its being full of holes (7)
I believe the answer is:
Here is my best explanation:
'being full of holes' is the definition.
'on the day dead annoyed about' is the wordplay.
'on' is a charade indicator (letters next to each other).
'the day' becomes 'd'.
'dead' becomes 'd'.
'annoyed' becomes 'riled' ('rile' can be a synonym of 'annoy').
'about' indicates putting letters inside.
'd' after 'd' is 'dd'.
'dd' placed inside 'riled' is 'RIDDLED'.
'its' acts as a link.
I am not very happy about this link. It may belong to another bit of the clue.
(Other definitions for riddled that I've seen before include "spoken obscurely", "Spread throughout", "Pierced with many holes as by tommygun", "screened" and "didn't talk plainly".)