Actually, to be fair, the weakest version is the one Waley praises by Cleaves in his prologue; so, 2nd weakest. This book is a compilation of the poems, articles, and translations of Arthur Waley, a Chinese & Japanese language scholar who also translated The Tale of Genji. Before you buy this book I suggest you Search Inside and check out the table of contents, because Waley's The Secret History (TSH) only involves pages 231-329. Because of this I feel the title of the book "The Secret History of the Mongols: A Saga of Epic Battles, Betrayal, Love, Tyrants, and Prisoners in Ancient China" is poorly chosen, hence my 3-stars. The title implies that TSH is the focus, when in fact the focus is on the works of Mr. Waley, of which TSH was but one.
I personally have little interest in his other work, so my review focuses on the 98-pages (out of 355) dealing with TSH, and I do apologize if you were looking for information on the rest. If you have a basic interest in reading TSH, the version by Paul Kahn is both affordable and more than adequate, and is written in the original poetic. If you are looking for a more in depth study of this subject, then without a doubt I would recommend the 2-vol set by Igor de Rachewiltz as the definitive study.
Aside from all the extraneous works in this version, there is another issue potential buyers should be aware of: it is not the complete TSH, it is only excerpts. It is also not in the "original" form, which was prose, but rather a translated version that only recounts the story-tellers' tales. For some, especially people who just want the gist of the story, Waley's translation will likely be more readable and user-friendly, which was his intention when he wrote it, but for the purist it simply won't do. With regards to this aspect, Waley does a good job as he referenced both the Chinese and Mongolian versions for his translation.