Is it just me, or am I being over-sensitive when I become uncomfortable when a husband/wife squabble over a little issue in front of other people?
Is it best for a married couple to work out their disagreements in private?
Is it ever justifiable for a married couple to disagree with each other in front of others?
Back to your original questions:
Seeing a couple squabble over little issues might be embarrassing, but I don't think it is worth becoming sensitized or uncomfortable about. Squabbles are part of the Fall--we don't always have the ability or inclination to deal with one another in grace. It doesn't mean it's right, but we acknowledge other things like jostles and bumps as being inevitable--likewise small squabbles.
But I know what you are getting at. Abusive arguments in public are unseemly. Belittling your spouse with insults is a violation of the 5th Commandment and even unconverted everyday folks find it uncomfortable and inappropriate. We all feel embarrassed for the couple, and a little nervous for what else they might do, as they apparently feel little to no shame.
The big deal is respect. I don't think it is ever appropriate to publicly or privately humiliate or insult a spouse. But disagreeing in public in a civil fashion is fine and expected, of course, depending upon subject matter.
For example, a couple shopping: suppose husband really wants to go look at the tool section of a huge store, and then get a pizza, while his wife is nauseated with a migraine. Should she be prohibited from expressing disagreement over how they spend the evening?
On the other hand, I'm fairly certain none of us want to hear an in-public disagreement over private matters.
It is all subject to a proper use of a sense of shame.