Why do you think Don keeps his box in his closet? He knows Betts could easily find it. Why not in the tool shed? (Isn't that where men are supposed to keep their secret stashes? )

Plus, how come there were dog tags for both Dick Whitman and Don Draper? I thought Dick exchanged the tags, so that the real Draper's body would be found with Whitman's tag and Dick could be honorably discharged as Don.

Good questions, Citrine.  Why didn't he completely get rid of Dick Whitman?  I'm pretty sure that's what I would have done.

Does he just not think that Betty roams around during the day with curiosity?  Does he think Betty doesn't see the drawer?  God, that is stupid.  But men were in those days.

"Men were [stupid] in those days," Becky?

That's offensive.  Men designed and constructed all of civilization.

WB: Men and women designed and constructed all of civilization! 
Am I imagining this, or didn't someone give Don (Dick) Dick's tags in the hospital? Why do I remember that, maybe I'm projecting.
But for your question Citrine, I've wondered the same thing!  I think Don simply thinks his space is sacrosanct, and Betz wouldn't dream of violating it- but then I think that he chose her BECAUSE she is, under the perfect surface, kind of dark, and hides her true self also.  So he should have hidden his stuff better.  Maybe he wants her to find out??

Uh oh, I meant no disrespect.  I think women were stupid then too in many ways.  Technology has made us savvier, though not necessarily smarter.

Quite so, Becky. We have knowledge, but not necessarily wisdom.

As to the dog tags, probably they were given to the Whitman family.  Adam kept them in the box with the pictures and sent them all together to Don.  As to why Don would have added the Draper tags to the box?  No idea.

Jack beat me to it.
Don received a Purple Heart in the hospital.

Don assumes, incorrectly, that his home office and desk are private. But Betty is like a child who lets her frustrations get the best of her.

What episode did we see Don receive the purple heart in the hospital. I am thinking I must have missed a few things in season 1

Season 1, Ep. 12, I think.