I don’t know if I can consider myself an AR “connoisseur” but assuming the rifle is assembled and functions properly, the first thing I look is if it’s configuration fits what I plan to use the rifle for. After that, I look at the quality and specifications of the barrel. The barrel is the foundation of the rifle. I check for rifle twist. While the 1/9 is a good choice if the shooter stays with shorter bullets, I think the 1/8 & 1/7 are better choices for my use.
I will pass on M4 & government profile barrels. Not because they are bad, I just don’t want the M203 cut of the M4 or the poor weight distribution of the gov.
The one barrel profile I’d like to see is what is commonly called the “sporter” profile, like what’s found on hunting bolt actions. It would be just a little thicker and heavier than an AR lightweight or “pencil” profile.
If there is anything on the rifle that shouldn’t be, or anything that adds unnecessary weight, I lose interest. Gimmicks are a no-go. I will check for fit & finish and examine the small details. While the cosmetic aspects of fit & finish do not make a rifle shoot or function better, proper fit & finish and attention to detail tells me whether or not the folks who made it “get it” or if they are simply hamfists trying to make a buck
Does it have quad rails? Standard M4 stock? A1 upper? Vertical foregrip? Pass. None of these items affect the quality of the weapon nor are they bad features, they’re just not what I want to spend money on. (Quad rails are not a complete deal breaker. I would buy a KAC SR15 E3 because I like how it handles. Otherwise, I would choose standard handguards over a quad to save money and install a FF handguard I like.)
Low quality optics, mounts & rings? Low quality furniture? Pass.
I will look to see how the rifle shoulders and how it feels in my hands. If the fit, feel or balance is awkward, I’ll pass.
The hardest thing to explain and is strictly a personal quirk, I look to see if the firearm- any firearm- talks to me. If it lays in my hands dead and inert, I will pass. There needs to be some sort of tug before I buy. Strange and probably useless in answering your question, but it’s a factor