Not had a light saber appear in game yet. I wonder if they "scream" Jedi to everyone though. Han and the other cantina patrons did not all immediately seem to suspect Kenobi of being a Jedi in the Cantina, although they certainly found the saber unusual. Similarly on the Falcon Han sneers about "Hokey Religions and Ancient Weapons".
This and a few other things make me suspect that contrary to the prequel trilogy the Jedi were already fading when Luke was born. Twenty years from Palpatine taking power to New Hope beginning is not a long time for the Jedi to be completely forgotten, or is it? Certainly I can see new innovations being adopted that quickly and people forgetting what life was like before them, but it seems quick to forget something that had existed "for a thousand generations".
I still go back and forth as to whether they were Jedi exclusive or not.
Well, the lightsaber was a pretty iconic weapon of the Jedi Order, with other users being even more of a minority in the galaxy than a Jedi Knight.
As for the cantina scene, the patrons probably figured they were better off not screwing around with the old man that just cut down two dangerous men like it was no big deal. Sort of how if you were in a seedy bar and saw Glenn Jacobs (aka WWE's Kane) choke slam some annoying jerk through a table, you probably wouldn't be in a hurry to screw with him.
In regards to Han's derision during that fateful trip to Alderaan, that was probably a mix of a 20-year Imperial smear campaign and Jedi already being near-legendary figures (before the Clone Wars, there were 10,000 Jedi Knights and Masters, which in a galaxy with trillions upon trillions of sentient beings is a tiny percentage of the galactic populace). So never having seen the Force in use, it was easy for Han to laugh it off as "smoke and mirrors." Had Kenobi opted to bust out some telekinesis or Jedi mind tricks, Han might not have been so quick to dismiss it. I'd imagine Han was fairly dumb-founded when Vader stopped those blaster bolts with his gloved hand in ESB before using telekinesis to disarm Han of his trusty blaster pistol; the most Han had likely seen of the Force before that point was Luke doing what amounted to "parlor tricks," especially if you take into account his skepticism of Luke being a Jedi Knight in RotJ.