They've pretty much covered it. It all depends on how common evil alignments are in your game. Also, it depends on the public reputation of paladins. If a paladin is widely acknowledged as a law unto themselves, the valient, unquestionable defender of the masses, they're not likely to be bothered. If this is an area where paladins aren't seen that often, or if they're not considered above the law, a paladinbot could run into problems. Smite the evil person, get arrested by the Lawful Good guards for cold-blooded murder. "But he wouldn't have detected as evil if he didn't deserve to be smitten, er, smited, um, I mean, killed!" "Yeah, yeah, we get that all the time. If you had evidence on him you shoulda called the guards. Tell it to the judge."
Also, what if the paladin detects evil in, say, the local sheriff, or baron, or the king's most trusted advisor, or the king himself? What if the paladin momentarily detects evil in the high priest of the temple he follows, but then it "goes away?" Did he just bypass an Amulet of Nondetection? Was it a fluke?
Detect evil is a great radar for dungeon crawls. Despite appearances, it's not all that great in urban areas or for murder mysteries.
Isn't it interesting, in the real-life mystery genre, how often it is that the murdered individual was scum and had it coming? And the detective still goes after the person who killed him and makes the arrest becuase "murder is wrong?" Keep the Law in mind, Mr. Paladin! Might doesn't make right!