If you're a LG paladin and someone approaches you with a shady job - don't you now know about a potential crime against law and goodness that you should be thwarting? Would it be worth playing along just to find the other players and bring them to justice?
That depends on a lot of factors; hunting down absolutely every single lawbreaking and/or cruel act results in Chronic Hero Syndrome, wherein you get neither rest nor major work done because you're constantly detouring to fix everything. Superman can pull that off because he travels faster than sound (AFAICT), is essentially invulnerable to all harm, almost impossible to tire out, and (often) is both highly intelligent and nearly clairaudient (that is, capable of hearing/sensing things hundreds, even thousands of miles away). A "real" Paladin may have a deity's favor, but she's not a Kryptonian under a yellow sun; by having limitations, she
must prioritize, and
must occasionally refuse to deal with real issues for one reason or another.
In this case, the value in double-crossing (or exposing, or whatever) a dastardly scheme needs to be weighed against other pressing concerns. If the Paladin is not currently occupied with anything, or in fact is
looking for things to deal with? Sure, she might go after it because a potential crime, or even a serious atrocity, could be averted and that is a Highly Valuable Thing to a Lawful Good Paladin. On the other hand, if it's simply a "guard this stolen merchandise" kind of job, while she has a quest to end a terrible and supernatural evil (and, therefore, an evil which only she and those like her are
capable of dealing with, while others could deal with the stolen goods)? Priorities almost surely dictate that she hand such a task off to another legitimate authority, or even let it go, as she does so many other issues, because
she can't be everywhere at once and solve everything. Care must be taken with such reasoning, always, because "I can't solve everything" can easily become an excuse for apathy; but the converse, "I *must* solve everything," isn't really acceptable either.
Sir Keldorn, of the Most Noble Order of the Radiant Heart (in Baldur's Gate 2), is an excellent example of a Paladin who understands that there are, and must be, priorities. He will engage in duplicity (e.g. lying about who he is, in an oblique way) if it will pursue a just end. He will ignore minor crimes and indecencies when lives are at stake or other problems emerge. He addresses his concerns about (most of...) his companions' behavior with a mild, diplomatic demeanor--and generally lets those issues slide without pressing them further. (I say "most" because he's rather racist toward Viconia if they're both in your party, but that's hardly surprising.)
A wise Paladin has a difficult path to walk, and will probably wish that he could do more than he is capable of--but will recognize that limits force one to have priorities, and well-constructed priorities force one to occasionally refuse to do a small good so that a large good may be done instead.