It went a bit further than that, though. Pete had a college friend who worked at the DOD, and he asked the college friend to look up Don Draper's service record. Several things about it were off, so Pete knew that whoever else he was, he wasn't Don Draper. (The photos referenced "Dick" but nothing more than that; so it is possible that it could have been a nickname; it was the dates on the photos that did it. Based on the dates on the pictures, "Dick" could not have been old enough to have been an officer during the Korean War.)
I've often wondered about what Anna told her family about Dick vis-a-vis her husband Don. I don't think that she told them the truth; I suspect that she told them that he was a relative of her late husband's who had felt bad about his death and offered some support in addition to the Army pension, and introduced him as Dick Draper. That way all of the paperwork would line up with the lie. As Don pointed out, the fly in the ointment would be the real Don's siblings/parents, though I'm thinking that there must not have been very many of them, or Dick would have known something about them based on Anna having to run some interference with them.
My favorite line from this ep was when Joan said that "Greg dying is NOT a solution to this." Well, actually, Joan, yes, it would be; probably the best solution, actually. Also, how on earth could 7 weeks have been disastrous in 1965? There is no way that she could not have explained away a due date that was "off" by no more than 4 weeks. There was no ultrasound back then, no doctor would even test you until you were at least 8 weeks late. (Which is, of course, how we came to say that pregnancy lasts 9 months. It actually lasts 10, but in the old days you had to be at least 2 months gone before they could get the condition confirmed.) There were LOTS of very big and bouncing "7-months" babies in that era. (Actually, there were lots of very scrawny-looking full-term babies, too. My sister had a baby almost exactly at the same time that Joan's would have been due, and I remember that most of the full-terms at the time were well under 7 lbs. Doctors tended to encourage Mom's to diet a lot at the time, and smoking was still more common than not. All she would have had to have said was that she didn't follow her doctor's diet recommendations, and everyone would have believed her.)
Oh, and Lane is so darned dashing? Tee-hee.