Harry's accent gets thicker and thicker as he's succumbing to the Truth Serum, and the way he constructs his sentences gradually begins to sound more like German than English.
Remember Dana in the beginning of the movie managing to steal Harry's partner's money from his coat without them knowing? It comes in handy when she steals the key to a nuclear warhead while being hostage to a room full of terrorists without being noticed.
Whatever elite spy organization Harry works for seems to be amazingly tolerant of their agents using a lot of money, time and resources to stalk their loved ones. Harry's partner does point out repeatedly that he shouldn't be using agency resources for his personal issues, but Harry doesn't listen. When his partner flat out tells Harry he cannot call on-duty surveillance teams to follow his wife, Harry reveals he knows his partner screwed up a big operation because he was getting sex from a hooker, and kept quiet about it. This results in the partner having to cover for Harry with the never-seen Big Bosses a lot. It seems a lot of other agents, contacts and assets owe Harry favors (or he has leverage over them) that he can call in at his discretion. Which is actually not unlike real world spy networks.
Also, Harry and his wife, presumably, sometimes have sex, which presumably involves both of them being naked together. It stretches credulity to believe (especially given the nature of Harry's assignments in the film) that he has never picked up any scars or injuries on his body that she might notice and wonder what her husband has been doing to get them.
Harry's a convincing and charismatic liar. Considering his cover, he probably made up an extremely long, extremely detailed, extremely boring explanation for how he picked up the scar by falling on the luggage turnstile at the airport, to the point that Helen would have probably tuned out and just figured that even Harry's hurting himself was dull.