Was I right about this dining set I did Not get on Craigslist?  

Hmmm
These look like later, derivative designs to me... possibly 70s or 80s. The chairs are "Moller-inspired".

Very handsome
pieces, no matter what (or when). The doors seem to be solid wood, judging by the grain . . .

Oh good, thank you, I hope...
Oh good, thank you, I hope you're right, since that way I feel less disappointed! (Did I mention it was dirt cheap?)

SDR, do you say that because ...
SDR, do you say that because the grain is not book matched?

The plinth base on the sideboard
is a clue to its vintage. They are cheaper to make and were a lot more common on later pieces when companies were cutting corners.
I think also the rounded edges...? Does that have to do with easier veneering?

Thank you.
And is the way you determine the chairs are not Moller the thickness of the wood on the rungs? Maybe a lack of rounded, tactile quality? Or something else I'm missing?

.
woodywood: the chairs are not "Møller-inspired", they are "Møller-made", it's the model 85.

The model 85 has round legs, ...
The model 85 has round legs, and crisper edges on the seat back.

This is making me feel good,
that there's some disagreement about the chairs. I thought they were Moller 85, but a few things made me hesitate, including the things I mentioned above, and also I thought the tops of the legs appeared half squared off and half rounded, whereas the Moller chairs I saw on the web seemed to have cleaner flat tops.

Definitely not Møller chairs!
Definitely not Møller chairs!

That's right,
chelle. Also, you could look for the end grain of solid wood on the top edges of the doors . . .

I'd put money on veneer, SDR.
You and I both know that there's no way a solid panel that size stays in plane without a properly proportioned frame or battens to restrict it.
Random-flitch leaves is a good indicator of middling quality at best. I'd also guess late '70's/early '80's vintage.

As per the current JL Moller website . . .
. . . Model 85 was designed in 1981. Ergo, this "inspired" chair design probably surfaced within a few years afterwards.
It's always nice to still have active companies of mid century designs around for reference.
http://www.jlm.dk/

OK, so what do you see that tells you instantly --
Not Moller? I appreciate it.
And by the way, that link above shows chairs totally different from the 85s I've seen