I've done shows since 1988, but custom shows are far different from concours. I did assist my Dad with Corvette events, and one concours event with my wife.
That event was in St. Louis with my wife's 92 Jaguar XLS V-12 convertible. It took fourth with a 99.64/100.
One funny incident involved a guy who entered the event every year and could never beat his competitor. So that year he showed up with a brand new model...and STILL got beat by the other guy!
As John said..."clean, clean, clean". Don't think that they wont lift your floormats either. Get those air vents, the crud around the console switches, and try to get that loose change out of the shifter gate...and get that errant McDonald's french fry out of the seat rail!
Everything must be in working order (a tough challenge for Jags :p ).
Again, attention to detail and factory specs is the key. No silver painted parts where anodized parts would be, and no GM hose clamps where german ones should reside. Show up with an aluminum wing and you are history!
For things like batteries (that you mentioned), I used to keep all of the OEM parts and swap them out for shows. When the show was over, on went the aftermarket stuff.
The level of scrutiny however is dictated by the severity of competition. I attended a Corvette event where two cars were so equally matched in points that they had to give the win to one because the other had excess "lint" on the tires!
I did my last show in '97...family life took a front seat.
And keeping a creampuff nice at all times is a real pain!