With the exception of the De La Rue issues, I have only a limited collection of New South Wales.
I do have a fair bit of literature, including Hutson's book which is still the go to reference. The following information is from his book.
I've included a generic picture of each type under each description. The mint stamps are not mine. I'll break the information up over two posts to prevent potential glazing out.
The paper for the watermarked Laureates and the early Diadems is watermarked with a double-lined numeral that matches the face value of the stamp.
The 2d Laureate is known with the watermark inverted. It is rare. SG84-86; Sc.24
The watermark for the diadems is often found inverted and reversed (ie: the paper was printed upside down and the wrong way around). Reversed, inverted or sideways watermarks are really rare. SG88-101, 107-118, 131-172, 174-181; Sc.26-42, 44
Some of the early 1d and 2d De La Rue issues have a single lined watermark again matching the face value of the stamp. For the 1d and 2d, Hutson states the watermarks can be found in all four positions, some rare. He makes mention of the 2d with '1' watermark upright as a rare stamp. SG186, 191-94, 195-99; Sc.47-48.
For the 4d, he says he had this stamp with watermark inverted and no watermark. SG203-4; Sc.50
In 1871 a new paper with a watermark of a small crown over NSW appeared (SG Wmk 36, Scott Wmk 54). Except for some of the diadems the watermark is rare in any position other than normal upright. The following are mentioned in the text:
Perf. 13 1d, 2d, 4d, 6d, 1/- watermark inverted; 3d watermark reversed; 8d all four positions, common with marginal watermark
Perf. 10 1d salmon watermark inverted; 3d all four positions; 5d reversed and inverted is common
Perf. 13x10 1d salmon watermark inverted
Perf. 12x10 3d & 5d watermark in all four positions; 9d watermark reversed
In 1882 the watermark large crown over NSW appeared (SG Wmk 40, Scott Wmk 55). The diadems can be found in all four positions, otherwise the watermark is almost always normal upright.
The following are mentioned in the text:
Perf. 10 6d and 1/- watermark inverted
Perf. 11x12 comb 4d inverted (not scarce) & 1/-
Perf. 12 6d inverted (not rare)
Perf. 12x10 6d inverted
Perf. 12x11 single line 6d inverted