I am citing a Dutch work from the late 19th century. Not surprisingly, the spelling differs from the contemporary spelling. In APA, how would I use [sic] in such cases of old spelling? In the guidelines it is advised to "insert the term sic in italics directly after the mistake". It seems dull to me, though, to insert [sic] after each word that is spelt differently.
[sic] is only used in the case of an actual error in the quote. For example:
He said that they was [sic] calling him.
However, in your case, it seems there is no error, just a change in spelling.
I would never use it in the following example, where the quote uses a different form of English (British) from the one wrapped around it (American).
While my favorite color is red, she wrote to me 'my favourite colour is green.'
Likewise, if I were quoting Old English, I would not consider it an error within a quote if the quote was written in correct Old English.
In short, you should not use [sic] unless there is an actual error in the quote.
Yet another possible way to handle your problem is by way of introduction. In other words, instead of merely saying:
As Vanmulken wrote: "Though the fallen curry favor, the publick disregard it much."
you could say:
As the Dutch philosopher Vanmulken wrote in 1871: "Though the fallen curry favor, the publick disregard it much."
With a casual mention of the author's nationality and the time period of the quoted material, most readers will be able to figure out the reason for the "olde" spelling, without drawing special attention to it.
[sic] is reserved for mistakes as you state. Old spelling is not a mistake. You could, for example use italics for the words that differ from modern to signal to the reader that something is odd. To make such signalling clear you should tell the reader early on that this is how you have chosen to deal with the problem. Alternatively you do not signal at all and simply "warn" the reader that old spelling of words will be included.
If footnotes are allowed you could footnote the spelling the first time it occurs and provide some information on the word. This is more of a service and will not fit all formats for publishing so I mention it as an idea.
So you can come up with less obtrusive ways to deal with the old spelling. Using [sic] is as far as I can see wrong in the context of what you are doing.
As others have said, such usage of [sic] would not technically be correct, and I agree it would be distracting anyway to insert if after each and every applicable word. You could add, in square brackets at the end of the quote, something like [original spelling], similar to this type of usage:
Do not put quotations in italics unless the material would otherwise call for italics, such as for emphasis and the use of non-English words (see the Manual of Style). Indicate whether italics were used in the original text or whether they were added later. For example:
Now cracks a noble heart. Good night sweet prince: And flights of angels sing thee to thy rest! [emphasis added]
To denote archaisms and dialect A sic may show that an uncommon or archaic expression is reported faithfully, such as when quoting the U.S. Constitution: "The House of Representatives shall chuse [sic] their Speaker ..." Several writing guidebooks discourage its use with regard to dialect, such as in cases of American and British English spelling differences. The appearance of a bracketed sic after the word analyse on a book cover led Bryan A. Garner to comment, "... all the quoter (or overzealous editor) demonstrated was ignorance of British usage"