I'm struggling to tie up the loose ends with the last couple of clues.
1d - It looks like the extra letter should be W but isn't "That" more like 'something' than "What" - or have I got it wrong?
8d - Apart from the definition "by accident" I cannot parse a single letter of my answer but I'm pretty sure it's a group of extra letters.
15d - It looks like N is the extra letter but I've got TH in a 4 letter 'small lake' but then an ED at the end? Unless it's "got into small lake" and so that could account for the ED but then that would remove the inclusion indicator - and then I've got NTH for "peg" ?
I'm going round in circles - help!!!