Rhialto's story ruined Dying Earth for me.
Now for something a little less dramatic, Rhialto the Marvellous did away with the very thing that made Dying Earth so appealing. Its very namesake, the pervasive tone of it's inhabitants moods and actions. The feeling that at any time the sun may go out, stirring an abject fatalism in the waning earth's inhabitants. This message is conveyed quite beautifully, by observation of the principal characters and exposition by men of ancient knowledge.[1-2]
"...these people of waning Earth, feverishly merry, for infinite night was close at hand, when the red sun should finally flicker and go black." 
"Earth," mused Pandelume. "A dim place, ancient beyond knowledge. Once it was a tall world of cloudy mountains and bright rivers, and the sun was a white blazing ball. Ages of rain and wind have beaten and rounded the granite, and the sun is feeble and red. 
It's a wonderful way to ingrain into the reader the tone of the book and the perspective of those living on a planet soon to go dark. It is further reinforced by the motivations of Etarr, the hurried squabbling of Cugel and even the day to day affairs of townsfolk. [3-5]
"No," answered Etarr, eyes far away across the moors. "What is revenge? I care nothing for it. Soon, when the sun goes out, men will stare into the eternal night, and all will die, and Earth will bear its history, its ruins, the mountains worn to knolls – all into the infinite dark. Why revenge?" 
But you are young; thirty or forty or fifty years is not too long a time to wait."
Cugel put his hand to his abdomen to quiet the fretful stirring of Firx. "In the space of so much time, the sun may well have waned. Look!" He pointed as a black flicker crossed the face of the sun and seemed to leave a momentary crust. "Even now it ebbs!" 
"I will make you boots to last your life's span or until the sun goes out, whichever is sooner. In either case, you will lack all further need for boots." 
Dying earth is a marvelous place filled with ancient wonders, untold knowledge and civilization perched on the precipice of non-existence. It is a world where the inhabitants care not for these things for the common understanding that their sun will soon die and their earth will follow. They are pragmatic and nihilists and I cannot help but admire how well it worked.
But then there was Rhialto's story. SPOILERS are to follow so be warned.
If you're not familiar with Rhialto's tale and have no inclination to read it here is a brief summary. Rhialto is in a coven with a bunch of other full fledged Wizards who are quite powerful, the actual limits to their power are not clearly defined until later chapters. They spend their time with petty feuds among one another coveting each other's precious items, including Ioun stones. By the way, this is the origin of Ioun stones. This is all fine and dandy, capricious wizards that care more about their petty conflicts than the soon to be dying sun is perfect. That is, until Morreion and the last bit of the book.
Until that time there is a time-traveling venture, however to do so the Wizards had to make use of bound Sandestins who were of great power but also exceptionally fickle.. This was when I first began to think, well who cares if the sun is going to go out if you can simply choose an earlier time period to settle down in. Well, it was actually quite a fun adventure, we see that cultures changed drastically over the aeons and a civilized gentleman like Rhialto would prefer company in his own time. Very well. We also have a long journey of folly and foibles that reminds you of Cugel's eccentric adventures. We also see that time travel is far from exact and there are plenty of dangers to go along with it. That's all fine and good. Then we get to Morrerion.
Morrerion is a magician of legend who engaged alien creatures that were actually from another world (hmm) and the current cast is having such difficulty remembering him. So they turn to the legends and deduce his location which happens to be at the edge of known space (hmm). Then they move into a castle of their fellows which then proceeds to blast off into space. Wait, what!? Since when can people leave this dying rock whenever they damn well please? Doesn't that ruin the whole nihilistic tone of the last 500 hundred pages? Now I'm fine with ancient technology, in fact I loved the bit where he off-handedly described an elevator, and a Wizard living in a space shuttle is pretty neat. However, this was no ordinary shuttle, it could travel around the universe, it's propulsion was mysterious at best, it had it's own Trekky holo-projector, and it could come and go wherever it pleased. It was beyond silly and did not fit the rest of the book at all. In fact it retroactively lessened my love of the series.
So I will caution you, if you are currently reading Tales of the Dying Earth, skip the last chapter.
 pg. 9. Turjon observing the festival in Kaiin.
 pg. 33-34. T'sais calling upon Pendelume the Bargainer, keeper of knowledge and master of all spells.
 pg. 46. T'sais' encounter with Etarr, a man cursed by a sorcerous witch.
 pg. 146. Cugel trying to secure the titular Eye's of the Overworld
 pg. 417 Cugel's adventure's with the boots of levitation.