How would you search for the common error in recording an individual's reluctance: 'X is loath to do Y', which has replaced the correct English 'X is loth to do Y'

The latter is rejected by spellcheckers but it is, nevertheless, the correct spelling of this old English adjective.

You can use wildcard * in Google searches:

http://www.google.com/search?q=%22*+is+loath+to+*%22&btnG=Google+Search
- 123,000 hits

http://www.google.com/search?hl=en&safe=off&q=%22*+am+loath+to+*%22&btnG=Search
- 84,300 hits

http://www.google.com/search?hl=en&safe=off&q=%22*+are+loath+to+*%22&btnG=Search
- 308,000 hits

or more generally just "loath to":
http://www.google.com/search?hl=en&safe=off&q=%22loath+to%22&btnG=Search
- 1,180,000 hits

But I thought the more common error was "loathe to" (a truly grammatical error) instead of "loth/loath to", which are surely just alternative spellings:
http://www.google.com/search?hl=en&safe=off&q=%22loathe+to%22&btnG=Search
- 810,000 hits

Why do you believe "loath to" is incorrect? The OED lists them as equally acceptable variants, and gives examples of writers using both spellings back to the 16th century; beyond that there's an even wider variety of spellings of the word. Indeed, if you want to go on common patterns of OE -> ModE orthographic development, "oa" is probably the best-supported spelling: "loath" comes from OE "la:th" (with long back "a"), like "oath" from "a:th", "goat" from "ga:t", "boat" from "ba:t", "oak" from "a:c", "soap" from "sa:p(e)"...