In 1976,  Random House made a minor change to the covers of the Hardbound Trade Edition line. The covers went from a matte finish to a glossy finish.  The reason for the change is not entirely clear.  One possibility is that the change came when Random House changed manufacturers.  Random House used The Colonial Press, Inc. of Clinton, Massachusetts to manufacture their Three Investigators books up until about this time.  The Colonial Press shut down in 1977.  I would appreciate any accurate information from anyone who might know more about this or who the succeeding manufacturer was. 

All of the new Three Investigators titles published in hardcover between 1976 - 1978 (titles #24 - #28) are only found in the glossy cover format.  In addition to these five titles, eight of the earlier Three Investigators titles can also be found in the glossy cover format (#'s 4, 5, 11, 13, 16, 17, 19 and 20).  This occurred as the publisher's supply of the matte cover titles was sold through and new product was manufactured in the new format. In all glossy cover books manufactured in 1978, there is a list near the back of the books which states which books were available in paperback and which in hardcover.  Out of the 16 books listed as being available in hardcover, all can be found with the glossy covers except for #14 Coughing Dragon, #21 Haunted Mirror, #22 Dead Man's Riddle, and #23 Invisible Dog.  It is assumed that the publisher had a large amount of those titles printed up prior to the glossy cover conversion as they were still available in the matte cover format almost three years into the conversion.  1978 was the final year in which Random House produced any of the Three Investigators books in a hardcover trade edition.  

The following thirteen titles can all be found in the glossy cover format:

#4 Green Ghost  - lists to #26 on back cover, white endpapers

#5 Vanishing Treasure - lists to #26, white eps

#11 Talking Skull - lists to #23, white eps

#13 Crooked Cat - lists to #26, white eps

#16  Nervous Lion - lists to #26, white eps

#17  Singing Serpent - lists to #26, white eps

#19 Phantom Lake - lists to #22, blue graveyard eps

#20 Monster Mountain - lists to #22, blue graveyard eps

#24 Death Trap Mine - lists to #25, white eps

#25 Dancing Devil - lists to #25, white eps

#26 Headless Horse - lists to #26, white eps

#27 Magic Circle - lists to #28, white eps

#28 Deadly Double - lists to #28, white eps

On occasion, one will find Hardbound Trade Edition titles #10, #12, and #14 in a semi-glossy cover. These books have a cover finish similar to many of the GLB editions. One should not classify these books as true glossy cover books as they were not manufactured during the glossy cover years and they do not have a true glossy patina.  These semi-glossy books will list to either #16 or #20 on the back cover.  These books deserve further study and make an interesting addition to a completist's collection.

There is some speculation as to why "Phantom Lake" and "Monster Mountain" list only to #22 on the back covers.  Since production of the glossy covers wasn't full-scale until 1976, they should list at least to #25.  It is possible that these were the first titles given to the new (and currently unknown) manufacturer to produce as a test in early 1975.  These are also the only glossy cover titles which can be found with the blue graveyard endpapers (which also indicates that they were definitely manufactured before 1976) - each of the other titles is found with white endpapers.

Most of the thirteen glossy cover books are fairly difficult to find and obtaining a complete set of them in near mint condition is a formidable feat indeed!  Many of the glossy cover books tend to have cocked spines or cracked textblocks with loose pages.  Titles #20 and #26 are by far the easiest glossy covers to find.  Titles #24 and #27 are difficult to find but, based on my experience, I believe that #11 Talking Skull is the rarest of the thirteen glossy cover titles.  I would expect to see any Three Investigators glossy cover trade editions command premium prices, particularly when in near mint condition.  Pictured below is a complete set of the known glossy cover books.
A Complete Set of the Known Glossy Cover Books