One of my all-time favourite characters in this system was a droid with 4 brawn and 1s in everything else. The character had a wound threshold of 22 and a soak of 9, but because of a memory wipe (at character creation), he avoided combat. He insisted he was programmed for protocol and would always attempt to talk out of a situation or slice a security system. He did all the things he was mechanically bad at, and it was hilarious. When he did use his mechanically-good abilities, I always described them narratively as accidents. While trying to escape a fight, he turns to run, smashing into a minion group, knocking them unconscious. "I'm so terribly sorry, would you like me to apply first-aid?" and would then just make it worse.

The trick was, I had to consider what my actions would do to benefit or hurt the group, but I could narrate them however I liked. Sometimes, if the group wasn't sure what to do, all we'd need was an epic fail to move the story forward!

In hindsight, I'm glad I played a droid for my first character, because if I hadn't it would have probably taken me a lot longer to realize how little of a handicap a 1 characteristic is. Heck, if it'd clicked how easily skill ranks improve tasks for a low characteristic character, I probably would've left Cunning at 1 along with Brawn and Presence on my mechanic droid. Like ladyjulianne, I thought I needed it to be two to be decent at things (mainly Perception). So while I'm going to need to buy skill ranks in Cool to improve my initiative checks, I'm glad I left Presence at 1 to represent my droid's complete inability to understand and leverage organic responses.

I've had a total of seven different players in three games (several of the players played in more than one game) and none of them kept a Characteristic of 1 (they all paid starting XP to raise it). Oh, except for the guy that played a droid...but he very quickly decided he hated the droid rules and switched out for another character.

I just had this affect a session. I have a Togrutan Shien Expert, who has a 1 in Brawn, he suffered a "Hamstrung" crit in battle and they threw him in the bacta tank so they wouldn't have to wait. He ended up failing 5 checks in a row, to heal an (iirc) average difficulty crit. It was hilarious, and something we'll all remember for the rest of the campaign now.

I think that while there's nothing inherently "wrong" with running characters with characteristics of 1, there are some obvious things to take note of. First, when assigning characteristics scores, you need to ensure that your 1-stat comes in an area that you have no intention of getting good at in any way. Look at the skills that are linked to that characteristic and mentally wave them goodbye.

Second, and just as importantly, you need to come to terms with the fact that there will be one or two skills linked to that characteristic that you will most likely be required to make checks with more or less frequently. Brawn has Athletics, Agility has Stealth or Ranged Combat, Willpower has Discipline, Cunning has Perception, and so on. Then spend some XP to get that skill up to rank 3 or so. Then the low governing characteristic won't impede your character in the slightest when the call for those checks come up.

Typically 1 in characteristics repersents a major character flaw and I often have fun playing out the flaw, since it's a small spectrum of what makes my character who he is.

Tobin Stryder Rodian Gadgetter turned force Sensitive is a bit of a genius. Having developed an int of 5 and an agility of 4 and the rest as standard. As such he's the techie/hiest master of the team who's a crack shot. But his lack of pressence and will makes for some highly amusing moments when he tries to make an epic speech, only to kind of mumble something out instead that is entirely counter-productive.

-Interigating an ISB agent- "Look, we know where this Gelvin guy is, so where is your strike team?"

(Rolls one Will dice, rolls blank)

"Oh don't give me that, I know your knew to this kid since it's obivous you don't know."

"Your ri- SITHSPAWN!"

Or charming by attempting to pull that landmark Lando Grin...

"Dude, it doesn't matter how I look at it, your attempt at a grin makes me want to stick flowers in it and call it a vase."

Sure, I made the mistake of being over specialised but I turned that into a interesting set of traits.