The Complete Guide to Anachronisms in Samurai Champloo--
Hellhounds for Hire (Part 1)/Tacit Understanding
Episode 3: Hellhounds for Hire (Part 1)/Tacit Understanding:
The overhead lamps in the gambling den: These do not flicker and do not cast the same sort of light as the candle sconces which are also nearby. If they're oil lamps (which they seem to be in the one shot from underneath them we get in episode 4) I can't figure the closed shades; but it's really not likely that they're electric. Overhead chandeliers came into vogue in Japan in the Meiji period, but not electric ones... See anachronism notes on Episodes 15 and 19 for the idea that gaslight may have come into existence earlier in the Champloo universe than in our own Japan.
The giant animated crab over the door: I very much doubt big mechanical devices like this were used for advertising anywhere in the Edo Period. They're quite popular these days, though; at least two well-known restaurants, Kani Doraku in Osaka and Kani Shogun in Sapporo, have 12-foot-high mechanical crab signs over their front doors that are tourist landmarks. Real photos above are Kani Shogun on the right, Kani Doraku on the left. (I have a photo of yet a third which seems to be the actual model for the one in the episode, but alas, I don't know where it is...)
The fortune-teller's magnifying glass: The principle of magnification had already been around for hundreds of years, but a "Sherlock Holmes" type of hand magnifier like this seems unlikely--though I can't find a conclusive visual reference yet.
Rikiei's shades. More on these under Episode 4, but here's our first look at them.
Anachronisms Occurring Only in the English Dub:
--the restaurant proprietor tells Mugen that the yakuza are "made men"--a Mafia term that certainly didn't yet exist in Edo Japan, but it's appropriate, since it establishes that the guys are the period's equivalent of mob-style gangsters.
--Mugen's laid-on-thick slang: wassup, chill out, mofo and the rest; thankfully not used on the second volume, but really prevalent here.