Should the different branches know the basics of rank for all the other branches?

Yes I believe we all should know the ranks of the other branched but that probably wont happen it gets a little confusing. While in Iraq i had to learn the rank structure of their military and that to me was all over the place and hard to remember. Luckily most of their Generals wore plain cloths usually but had their ID out before hand and I could see the green strip on it far enough to lock up at attention and render the salute because we was supposed to treat them with the same courtesy as our own officers. They where actually pretty nice and spoke English very well also and would stop and speak to us from time to time and see how their guys that worked with me was doing. Really i think that there should be one rank structure across all our branches though to avoid confusion that happens so much.

I remember during Infantry OSUT, during the middle of training being given duty as human training dummies at the Eagle Skills Assessment (end of training testing). Because we were working the testing sites, the graders had us wear are patrol caps at the site...and every trainee was either trying to stand at parade rest or salute us. Even though all these testers were almost done with training and we were six weeks behind them, those trainees figured everyone out ranked them?

I like the idea of retaining the unique character of each of the services and thus don't like the idea of one rank structure across the services.
That said.
I do think everyone serving should know the rank structures of at least our own services and remember being instructed on and tested about those items of interest at a certain entry level training located in the environs of San Diego.
Now that's rank structure, when you start bringing rates into the picture not even all the Navy folks can keep up with all of the rates.
Allied or even Opposing forces are things I think forward deployed troops would WANT to be familiar with also.
Now, having gotten all of that out of the way and speaking with 6-7 years in Joint environments, an added benefit of knowing each services rank structures is that an equivalent rank doesn't necessarily equate to equal responsibility at each rank in each service and knowing these facts can tell you if you're talking to someone who has the authority to deal with whatever issue you may be working on. Their knowing your rank and service can also help them decide if they're comfortable taking action based on you and your rank or if they would prefer to seek comformation of your request a level up or not.
One might think that a unified rank structure would address that last paragraph, but IMHO, given the varying sizes of the services I can't see how that could work.(The following may not apply in all circumstances of course, but expresses my experience with the issue) As it is in the much smaller USMC an E-4 may have as much or more authority than say an Army E-6, Air Force E-6, or a Navy E-5. Would we then go thru then pains of elevating the authority/responsibilities given to those in the larger services or cause the Marines to suffer the indignities of lessening their authority/responsibility? I think neither should occur, but that being familiar with these peculiarities should definitely be learned by those who will encounter and coordinate with those from other Services. It can make your day much easier, especially if you extend that to knowing things like that an Army E-6 or E-7 might be fine with being called Sarge or Sergeant depending on your familiarity with them but a Marine E- 6 or E-7 are going to have a hard time even listening to you much less granting any requests you make after having just demoted them by one or two ranks, unless your request benefits them in some way or they're feeling especially tolerant that day. Also, Chiefs tend to simply ignore fools that call them Sergeant.