It turns out that most modern presidents do not give a State of the Union address in the first year of their first term. Bush didn't give one in 2001, Clinton didn't give one in 1993, Bush didn't give one in 1989, Reagan didn't give one in 1981, Carter didn't in 1977, Nixon didn't in 1969. That appears to be how far back it goes, generally. In fact, some presidents have given outgoing SOTU's rather than incoming, including Johnson in 1969, Ford in 1977, and Carter in 1981.
I think that the problem here consists in what one considers a "State of the Union" address. Incoming Presidents do usually give an address to a joint session of Congress in first weeks of their term, in which they outline the legislative programs they intend to pursue with the help of the Congress. Sometimes this speech is called a State of the Union address; sometimes it is not. There seems to be little consensus on this; C-SPAN, for example, does appear to consider these addresses to actually be State of the Union addresses. Now, they also provide transcripts of a few non-SOTU Presidential addreses to Congress -- President Bush's address after 9-11-01, for example -- but the "inaugural Congressional address" seems to generally fit C-SPAN's definition of the SOTU speech:
The president's State of the Union Speech defines his view of national priorities and needed legislation. Since 1913, presidents have chosen to deliver the speeches in person once a year, usually in January.
Interestingly, every President since World War II has given such an address to a joint session of Congress in the opening weeks of his term, with the exceptions of Presidents Nixon and Carter. Also interestingly, President Truman delivered no State of the Union message at all in 1952, despite the fact that his term ended in January of 1953. If this seems odd, it's worth remembering that the Constitution specifies no time frame for the delivery of a SOTU message. All the Constitution says is this:
He shall from time to time give to the Congress Information of the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient....
There's nothing there that requires a yearly, personal visit to Congress: the President could send them a letter every nine months if he so desired in fulfillment of these Constitutional requirements. Of course, the speech itself has a lot more weight as an event, especially in the television age, so that's the way it goes. This probably goes double for Presidents' initial SOTU addresses when they're only a few weeks into their Presidencies; since the Inaugural Addresses take place shortly after noon Eastern time, fewer people probably get to see them in their entirety than do the SOTU addresses, to say nothing of the fact that an Inaugural is more for "lofty rhetoric" than the type of policy stuff that holds sway in an SOTU speech.
So, anyway, I don't think the title of the West Wing episode constitutes an error.