The female soldier thing was a nice touch, if hyperbole (which is perfectly fine and expected in this sort of content imo). Classical Sparta did educate women, including physical education.
There are other things they could have done playing on Sparta's reputation. They could've made them laconic, for example, but they're pretty expressive and long winded imo. IDK. I think they could've done humor with making them all terse. Could've also done humor with Spartan motherhood/wife stereotypes, e.g. "come back with your shield or on it."
I think those are stereotypes of Sparta that we carry down to our own time and also present in classical Greek texts. I think they could've played with them. Maybe they still will!
Speaking of laconic, I thought you all were talking about Sparta when you talked about Laconia; was surprised to find it a specific town rather than a region. I mean the town still is associated with Sparta, so okay, but not what I was expecting. Glad that they in general showed Sparta throwing their weight around in the region.
A translation nitpick perhaps (and I'm playing the earlier one, not the recommended one, sadly) but the Athenians calling the Spartans barbarians is kind of weird, given that the term is explicitly about language and both speak a variety of Greek. But I guess the Athenians were being presented as being oddly crazy at the time or something.
Also a bit strange that slavery isn't being brought up in Sparta of all places, if it is going to be brought up.