Walsh hits minor character pay dirt: he isn't one of the most important characters in the movie, but he gets the biggest (and most famous) line.
He's one of Jake's two assistants, the other being a guy named Duffy. Walsh helps Jake conduct his investigation into Hollis, at one point spying on a conversation between Hollis and Noah.
If Walsh had managed to hear it, he might've blown the whole case wide open. As it is, he only catches one word, which he thinks is "apple core." In actuality, the word is "albacore"—the name of Noah Cross's club, and the organization he's using to support the retirement home that figures in his scheme to steal water (Noah registers the land to which he's transporting the water under the names of the home's residents).
At the end, after everything's gone bad and Evelyn's dead, Walsh walks Gittes away from the scene of her death, telling him:
WALSH: Forget it, Jake—it's Chinatown.
Walsh means that this situation has gotten so confusing and strange that they can't understand it anymore; it's beyond their control. It's not so much a racist remark against Chinese people as a reference to what Jake had said earlier in the movie—when confronted with a foreign culture in Chinatown, he was unable to understand whether he was helping or hurting the people he was meant to be protecting.
We can only presume that Walsh took him to Dairy Queen afterwards and got him a banana split for consolation. Hey, that's what we do when we're sad and befuddled.