Since I do own a first edition set, I'll add a couple of pointers.
My set (late impressions from the early 1960s) include the earlier appendices, but not the index or the sections on languages and calendars. These were added to the Second Edition, and, I think, to some of the American editions published between the British revisions. Tolkien simply hadn't completed them by the time he and his publishers decided to release RotK.
Just in case someone does think they've got hold of a first edition, here's a very brief description.
The first edition was printed by George Allan and Unwin in the U.K. in three hardback volumes, bound in red cloth. The dust-jackets are a pale cream in colour, with a design in the centre of the front cover depicting a ring with a red eye glaring through it, and the One Ring's inscription wrapped around it in red Feanorian script. The title of each volume and the author's name were printed in red and black inks, but were varied so that
The Fellowship of the Ring and
The Return of the King have titles in black, whereas
The Two Towers has its title in red.
The Two Towers also differed in the printing on its spine, in which the colours of the title and author's name (on the other two volumes, a black title with the author's name in red) were inverted.
The first edition maps are coloured, folded inserts in red and black ink, initialled by Christopher Tolkien, and they incorporate some variant spellings (such as 'Kirith Ungol' in the map to RotK). The volumes should also announce themselves to have been printed on octavo (8vo) paper, and bear prices on the jacket flaps of 21s per volume and 63s for the set (Tolkien wasn't wrong about the price: a guinea was well over a week's wages for some people in 1954). More importantly, they contain a completely different author's preface and will bear on the frontispiece the entire printing history up to the time of their own impression. Anything other than a first impression will announce the dates of subsequent printing runs of the first edition.
If you have a copy of RotK with slipped text, it's a rare copy and might be worth a bit, and first impression volumes in excellent condition are also very valuable. If the volumes are signed, the value is exponentially greater. Even a late impression set in good condition is still not cheap, so this is not the edition to be using for day-to-day reference work.
I've rambled on long enough, especially since most of this is available elsewhere. Here's
a picture of a first edition set in top condition.
p.s. Bump.