I hate to be seen disagreeing on my first post but i would like to adress two things that you guys have been talking about.
First of all the fact that the Parshendi shard bearer was looking at Dalinar's face could have a much more plausable reason. Dalinar was there when the Parshendi were discovered so it isn't hard to believe that some of them would remember his face. Also the fact that in a Shallan POV Jasnah tells her that Gavilar saw a Parshendi thrust his hand out as if to summon a shard blade. It could that same shard bearer who recongises Dalinar because he saw Dalinar during those first days or recognised him through his resembelance to Gavilar. As for the speaking Alethi -come on- the Parshendi were talking Alethi within the first few days of their meeting with the Gavilar's party.
The second point is my theory on why Jasnah is right and the Parshmen and maybe the Parshendi are the voidbringers or potential voidbringers. For this we must go back to Kalak POV he saw red, orange and violet blood on the battle field after the desolation. I am pretty sure that Parshendi blood is orange and assuming that also includes parshmen, their blood was there in the aftermath of the desolation but Kalak doesn't see any Parshendi or Parshmen. Also in the book its is implied that human kind fought the voidbringer in the desolations, Parshmen and Parshendi are not humans.
Ergo the shard-bearer recognised Dalinar from the intial expedition into Natanatan or through his resmebalance to Dalinar and it is very likely that Pasrhendi/Parshmen were the enemies in the previous desolation.
I'm sorry for being such a naysayer and ruining your fun on the topic, but i would have bothered me if I hadn't said something.