In A Guide to English Language Usage I say
Judgement is the usual spelling but some courts, the European Court of Justice for example, use judgment.
It seems that the situation is more complicated than that. As Margaret Marks explains on her Transblawg, in UK legal usage a judgment is a decision of a court while judgement is the ability to make a correct or wise decision. She quotes Lord Neuberger comparing and contrasting the two forms (my italics):
Judgments are the means through which the judges address the litigants and the public at large, and explain their reasons for reaching their conclusions. Judges are required to exercise judgement – and it is clear that without such judgement we would not have a justice system worthy of the name – and they give their individual judgement expression through their Judgments. Without judgement there would be no justice. And without Judgments there would be no justice, because decisions without reasons are certainly not justice: indeed, they are scarcely decisions at all. It is therefore an absolute necessity that Judgments are readily accessible. Such accessibility is part and parcel of what it means for us to ensure that justice is seen to be done, to borrow from Lord Hewart CJ’s famous phrase.
This distinction is not recognised by the COED:
judgement (also judgment)
1 the ability to make considered decisions or form sensible opinions. Ø an opinion or conclusion. Ø a decision of a law court or judge.
or by the OED, which has a number of quotations for judgment in both senses under a common entry for the two forms.
In Wikipedia I find this:
In a non-legal context, spelling differs between countries. The spelling judgement (with e added) is common in the United Kingdom in a non-legal context. In British English, the spelling judgment is correct when referring to a court’s or judge’s formal ruling, whereas the spelling judgement is used for other meanings. The spelling judgment is also found in the Authorized King James Version of the Bible.
In American English, judgment prevails in all contexts. In Canada and Australia, in a non-legal context both forms are equally acceptable, although judgment is more common in Canada and judgement in Australia. However, in a legal and theological context, judgment is the only correct form. In New Zealand the form judgement is the preferred spelling in dictionaries, newspapers and legislation, although the variant judgment can also be found in all three categories. Usage in South Africa is similar to that in Australia and New Zealand.
Whatever the dictionaries say, UK legal usage seems clear and I am just as content for the lawyers to set their own rules for the terminology they use as I am for chemists to do likewise. As my book is primarily concerned with British English, I will make an appropriate amendment for a future edition.
Wikipedia is confused about Rubens’s painting. It has an article entitled Judgement of Paris and refers in the first paragraph of the text to The Judgment of Paris
Finally, I am not aware of any difference between acknowledgement and acknowledgment. The COED’s entry is
acknowledgement (also acknowledgment)
while the OED has
Also acknowledgement (a spelling more in accordance with Eng. values of letters).
That is certainly true and my own style has always been to prefer acknowledgement.