These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Broken Base: Gaiman notes in the 10th Anniversary edition how this is one of his most controversial books, with many fans finding Shadow too unlikable and the plot too wandering.
Ending Fatigue: Some releases of the book just keep going. Depending on the release, the plot can be followed with two epilogues and a continuation through a spin-off short story. Firstly, the named "Epilogue" chapters appear to tie up the remaining loose ends and character threads; the "Post Script" chapter, which sees Shadow visit Reykjavik and briefly chat with the original incarnation of Odin; and then, in some releases, a few chapters that see Shadow visiting Scotland and taking on a single job.
Genius Bonus: Anyone who knows the origins of the names of the days of the week (etc. "Friday is Freyja's day") can figure out Mr. Wednesday's real identity pretty quickly.
Not only that, but in general the more mythology you know the more you will get. In a book that explicitly contains Norse gods it would be unusual for there to be two redheads with scarred lips, eh?
Hinzelmann is based on the legend of a kobold named Heinzelmann, whose true form was of a small child with two swords impaled in his body. Also, it was said that if he was ever chased out of his house, evil luck would follow. In the end, it's implied without Hinzelmann alive the town of Lakeside will no longer be the idyllic, slice-of-heaven town it is now.
Narm: In the 10th-anniversary edition audiobook version of American Gods, Mad Sweeney'sFinal Speech is ruined for Jewish viewers because the way he pronounces "boobies" is identical to the Yiddish bubby, or grandmother. What kind of fortune letter would let an old drunken leprechaun play with her grandmothers? Perhaps he just really wanted some Christmas Cake...
Nightmare Fuel: Hinzelmann. The story of the tribe that creates its own god from a murdered child, who in turn, a few thousand years later, settles down in Lakeside and kills another child each year.
Squick: Many examples: a man eaten by a vagina, the man-eating goddess being ground into a bloody smear by a limousine, almost any scene in the last half of the book involving Laura...
Media taking over Lucille Ball's image on an episode of I Love Lucy and offering to show Shadow Lucy's breasts. Thankfully, Shadow turns the television off before she can do it.
Wednesday getting half his head blown off. Followed by instant replay!
The Woobie: Poor Shadow doesn't catch a break throughout. When he finally dies by hanging from the World Tree for nine days, just like Odin/Wednesday before him, his last request is to be left alone in The Nothing After Death. Of course, that doesn't last long, since Eostr/Easter brings him back to life for the final battle.