He's a "technical expert on railroads" because he is what passes for an "expert" among the ruling gang - he knows at least the basics (what the lines are, what the basic uncomplicated blocks of running railroads are - from the same discussion as below quotes). Mostly, he's in the position of telling railroads what to do. There do not necessarily need be any qualifications, and by his own admission, he has no pretentions to having any:
"But listen, Clem, you know-you know just as well as I do-that we can't afford it!" Mr. Weatherby shrugged. "That's a problem for you to work out." "How, for Christ's sake?" "I don't know. That's your job, not ours. You wouldn't want the government to start telling you how to run your railroad, would you?" "No, of course not! But-" "Our job is only to see that the people get fair wages and decent transportation. It's up to you to deliver. But, of course, if you say that you can't do the job, why then-"
His job is basically policy, not technology:
"Right," said Mr. Weatherby. "That's what you ought to be-practical. Now we offer you a trade. You do something for us and we'll do something for you. You give the unions their wage raises and we'll give you permission to close the Rio Norte Line."
This is a common practice in totalitarian collectivist states (and happens even in modern democracies); the party apparatchik is appointed for their connections and ability to get the state desires properly communicated. Not a specific professional expertise.