I’m voting for Wonder Woman’s invisible jet. Especially when it was drawn as a series of dotted lines with Wonder Woman’s figure perched in the middle of it. Incredibly silly-looking.
Robin?
Any of Batman’s stuff from the 60s with the word ‘bat’ in their names other than the batarangs and batmobile.
The Supermobile. Supermobiles, actually.
In fact, any time a superhero other than Batman has a car, plane, boat, or whatever, that includes the active part of their name - the Supermobiles, the Spider-Buggy, and so forth.
Legion flight belts. (When they brought in the flight rings, it was so much of an improvement.)
Any of the Golden Age Sandman’s gear when he switched from a sleep motif to a sand motif.
Damn you, I was going to say that! 
Legion of Super pets?
Curses, foiled again!
Boxing glove arrow. I mean, how did that even work?
The Fat Fury’s lollypop.
Heck, there was even an aqua-lung arrow. Why Green Arrow and Speedy couldn’t just carry rebreathers or emergency oxygen cannisters without conforming compulsively to the arrow theme is unclear.
'Twere a Ray Palmer invention, naturally. In the quiver, on the bowstring, and for most of its flight the BGA looks like, well, an arrow. It had special sensors to detect when it was about to hit a human being, and a fraction of a second before impact, the boxing-glove part unshrunk to do the punching.
You think Robin was bad? How about Dr. Mid-Night’s owl, Hootie? Granted he eventually had a few hit songs, but as a superhero’s sidekick, it was as dorky it it came.
But, wait, there’s another: Static, the Proverb Parrot from the original AirWave. Basically, think of a avian version of Robin that quoted appropriate (and often mangled) proverbs as AirWave fought crime. The amount of help a 2-lb bird could provide in a fight is extremely limited.
Made of Supermanium, the toughest alloy in the universe! Wow.
How about Herby’s lollipop (from the ACG – American Comics Group – comic)
Actually, the dorkiest prop is the stupid Dial from Dial “H” for Hero.
The Spider-Car
Paste Pot Pete later renamed to a less dorky “Trapster” I mean, really! Your power is hot glue guns?
How about Rainbow Raider? I don’t know whether to make a gay joke or a Care Bears joke.
I know the OP asked about heroes, not villains, but damn!
Well, I’ll go to the foot of our stairs. I never new that. Ray Palmer, you say… now you explain it, it all seem perfectly reasonable.
Naturally, in light of this, I withdraw my nomination.
No, wait… it is still pretty dorky, isn’t it?
Naw. Her lasso of truth out-dorked the jet by a dorky dork-filled mile of dork.
Wonder Woman was created by William Moulton Marston and his wife. Marston is the inventor of the polygraph “lie detector”. it’s not surprising that she had a lie-detecting weapon. I’ll bet it was a lot more reliable than Marston’s real-life polygraph.
By the way, her invisible plane was incredibly dorky because it’s pointless. If you becanme invisible while flying in it, it would have a point. But WW was perfectly visible while she rode in it – if you looked up, you saw her flying through the air with no visible means of support, in a seated position. That has to be demeaning – the only ways to fly are either on a flyin carpet or with your hands stretched out in front of you, like you’re body surfing. Anything else makes you look like a dork.
So you have all the disadvantages of invisibility (can’t remember where you left the thing, have to feel for the cockpit. Can’t read the instruments. all the stuff they make fun of in Spongebob squarepants and elsewhere), and none of the advantages. Pretty useless. and dorky.
Wonder Woman’s invisible jet is pretty dorky. But is it as dorky as Arm Fall Off Boy’s, well, arm?