The edge of the plastic duct going to the upper vents is broken around where the steel push clip goes through. What's the proper way to repair this?

I have repaired broken tabs on plastic grills by getting a scrap piece of the same type of plastic and grinding it into small bits with a rough file and then mixing the shavings into a paste using acetone. Put the paste on in between the two parts and make sure they are stable while it dries. Once it's cured you can sand it smooth and paint over it. It's a very durable repair if you do it right.

Scott Smith Harms on here gets the credit for the acetone trick.

Do you have the corner piece? If not you may have to make one out of plastic that is the same thickness.

So does the acetone paste act like a glue for the piece you want to put on?

I need to find a piece of plastic to cut and shape first. I was thinking about an empty laundry detergent jug or perhaps a window washer fluid jug. The vent is made from a kind of waxy plastic often found in large kid's toys.

The vent is most likely made from abs plastic so you need to find abs for you repair so the glue will stick. Most molded plastics will be marked as to what they're made of. Most containers like laundry and milk jugs are made from polypropylene or polyethylene.
You could buy a piece of abs sheet from Mcmaster-Carr for a few dollars and use it for the missing part. You can shape it with heat to get it close and use abs cement to attach it.

I measured the thickness of the plastic with a vernier caliper. It was just under 1/16" so I tried using a window washer fluid jug to try to get plastic shavings with a course file because it was very close to the same thickness. I poured a little acetone just enough to make a slurry. It didn't dissolve. In the end, I cut a small piece from the washer jug and shaped it to fit. Then I crazy glued it in place. When it took, I used a wooden stick and then covered the repair area with seam sealer. I'll try to sand it tonight to see if it is solid. If it doesn't work, I'll try getting a piece of ABS plastic from Canus Plastics and bond it using ABS adhesive cement. Keep the ideas coming because I'll keep on trying things out until something works. Thanks. Lou

The washer bottle jug may be of a different material and that is why it didn't melt.

I think one time I had a broken plastic seat hinge cover and I used it to get the plastic shavings from. It melted in the acetone after a couple minutes. The paste it makes acts as glue between the two parts and once it's dry it fuses them together.

Plumbers pipe cement works on plastic too.

I have extra 71 ac plastic duct kicking around somewhere
that is made from the same material
if you are interested

I'm going to wait to see what happens. I've but the seam sealer on the duct and am waiting for the thing to dry so I can attempt to sand it. I'll have to drill a new hole too. This may possibly work. One thing I will need for sure is the special steel push clip that fits through each hole and secures the duct to the 2 Strato Vents. I'm missing one of those it looks like. Anybody have an extra kicking around?

So here is the end result and you can compare these to the original picks of the broken vent up above. The critical thing for me was making a correctly sized hole in the exact same spot. So I needed to take a round hole punch and pound it into the plastic. I wasn't sure if the assembly would explode or just be ruined but it turned out half decent. For those who are interested, I used 220 grit wet on the repair area. I used Dupli-Color black bumper coating to get the extra flex in the paint. I want to thank all of the contributors to this post because they really helped me come up with ideas on how to get this done.

easiest place for ABS plastic - black ABS pipe piece from Home Depot or Lowes . . . shave the pipe into the acetone and get a nice thick slurry . . . I would use a piece of wood (stir stick ??) for additional material, using the stir stick as the main structural component, covering it in the plastic slurry. Then let it dry for a few days, until all the acetone has come out and then drill your hole . . . but looks like you got it done . . .

That's all good for the next time I attempt an ABS repair. I happened to have a few black ABS pipe fittings that I could have used to make sacrificial savings for my repair but completely forgot about that until you mentioned it.

I'm still averse to drilling plastic. The holes never come out perfectly round. Given a choice, I'd take punching it out over drilling every time unless it's too thick. Then I'd drill.

when drilling plastic, a "step" drill works wonders. they don't catch like an ordinary bit. good to use in thin sheet metal, plexiglas, lexan, and fiberglass. the holes come out round every time unless you are real wobbly with the drill motor.

I've never used a step drill before. I believe I've seen them before and had no idea that their ability to create a perfectly round hole was so impressive. I must try that sometime.

Cheers.