Oh, Say Can You See?

It's in the correct order.

From NOAD:

say ... exclam. informal used to express surprise or to draw attention to a remark or question: say, did you notice any blood?

So think of that line being punctuated as:

O, say, does that star-spangled banner yet wave?

It's the equivalent of "Tell me, does that ... etc."

Statement "you can see" is reversed for a question "can you see".

The first four lines of the song are a single very long question. The core of the question is: "Can you see what we hailed?"

This question is then made much longer by adding a lot of additional phrases. Here I've marked the core question in bold, and the additional phrases with parentheses:

(Oh say,) can you see, (by the dawn's early light,) what (so proudly) we hailed, (at the twilight's last gleaming), (whose broad stripes and bright stars, through the perilous fight o'er the ramparts we watched, were so gallantly streaming)?

It's grammatically correct. It's like saying:

Wow! Say, can you do that again?

In the same way, in the anthem, "O!" is an exclamation, and "say" is being used as an interjection:

(used to express surprise, get attention, etc.)