I haven't solved the puzzle myself, so I assume everything is correct.
There are several places where you can fill in some black/background.
First the blacks (red spots)
column 7/8 row 33/34: Counting from the top in column 7, you can fill in 2 more spaces of the 15 clue, which automatically leads to the 2 blacks in column 8
column 39 row 12: counting in the row gives you one more black
column 33 row 13/column 34 row 12: counting from the bottom gives you a black in both columns
row 10 column 19: counting from the bottom gives you one more black
(the most important I saved for last)
row 14 columns 3/7/11/12: counting from left gives you 4 more blacks
column 30 rows 23/24/25: the black in column 30 row 22 cannot be part of the black 7 clue, so it has to be part of the black 10.
Now for the backgrounds (blue spots)
column 39: because of the black in the same column/row 12 you can fill in a background in this spot
column 13: 2 backgrounds because of the 14 clue in that column
columns 7/11/12: background because of the blacks in row 14.
The only tip I can give you in puzzles like this without any side-clues to continue easily, is counting, counting and counting.....
Good luck with the rest of the puzzle!!
Maarten
