Breen (1989) cited Proof examples for two varieties of the 1827 Dime.
Davis et al (1984) listed JR-8 and JR-10 as being known in Proof, the latter being a Proof-only variety. They also noted: "Proofs have been reported for [JR-3 and JR12], the latter in the Eliasberg collection, but neither variety has been seen by the authors in proof condition."
PCGS certified a PR-65 1827 Dime in 1988 and a PR-63 in 1999. Both coins have been cracked out and are no longer listed on the PCGS Population Report.
Auction records present a somewhat muddy picture. Six different examples emerge from a larger number of auction citations, plus a Proof in the Smithsonian. Further research is ongoing to determine the true number of surviving Proof 1827 Dimes.
The finest Proof 1827 Dime appears to be the Bareford NGC PR67*CAM that last sold in a Goldbergs 2/2013 sale for $86,250 (this same piece had a previous auction price of $120,750 in an NGC PR67 holder).
Sources and/or recommended reading:
"Walter Breen's Encyclopedia of United States and Colonial Proof Coins 1722-1989, New Revised and Corrected Edition" by Walter Breen (1989).
"Early United States Dimes 1796-1837" by David Davis, Russell J. Logan, Allen F. Lovejoy, John W. McCloskey and William L. Subjack (1984)